I’ve often puzzled over why students seem to struggle so much with angles - whether it be comparing the sizes of angles in diagrams drawn to scale, measuring angles or deducing their value. As I develop the angle waypoints for the Framework I’ve been forced into rethinking my own conception of what an angle is and what it can represent.
I’ve just finished a wonderful paper: Young Students' Concepts of Turning and Angle by Michael Mitchelmore (1998). The paper highlights quite how confusing angles are for our young learners and the variety of situations that we expect them to join together concepts of angle without explicit explanation. We work with an angle as a frame that we could model from wire, an angle as something more solid related to 2D space such as the corner of a shape, the angle view of a camera or spread of water from a sprinkler, and in movement, whether that be rotating an object or turning a corner. Pupils meet angles when discussing symmetry, properties of shapes, loci and constructions and carrying out transformations, to list just a few areas. Angles are sometimes constructed accurately and sometimes not drawn to scale. Even the language is confusing…why don’t left angles exist? The word LEFT even has a 90˚ angle in it – right at the beginning!
Mitchelmore suggests classifying angles in six ways:
Unlimited rotations: such as wheels and revolving doors
Limited rotations: such as the volume dial on your car stereo or a key in a lock
I-hinges: a linear object which is hinged about one end and can rotate between well -defined limits such as a door
V-hinges: two linear objects hinged at a common end point, such as the cover of a book
X-hinges: two linear objects hinged about a midpoint, such as a pair of scissors
Bends: two line segments with a common end point, where the turn is the result of moving around the corner formed. This one is a bit more difficult to imagine but if might help to imagine a turn in the road or an external angle of a polygon.
In addition to these categories angles can have a dynamic or a static nature (Magina, S., 1994). Are you looking at the final picture and measuring an angle – or watching the angle being formed?
In several of the categories above the angle isn’t explicit and additional line segments are needed in order to measure any angle; for example measuring the angle a door handle has rotated through. To measure the angle of turn you would need to identify the centre, a starting position and therefore define both the leg of the angle and the finishing leg (it’s difficult even to find simple vocabulary to explain these concepts clearly).
Other considerations include: the true representation of these angles; how to label them accurately and communicate precisely what is to be measured; how the degree unit is developed – and why 360˚? Moreover, when do angles remain invariant? For example, lengthening the arms of an angle doesn’t affect its size, and similar ideas can be explored in reflection, rotation, translation and enlargement.
These are the kinds of consideration that inform this very important area of the Framework. Mitchelmore suggests that the successful study of this area relies on the abstraction theory of conceptual development in the way that Piaget, Dienes, Skemp and others explain. Having spent 13 years in the classroom, it’s something I recognise in my learners. Abstraction begins when students can draw similarities between a class of experiences, and this similarity itself then becomes a new mental object. In other words, by experiencing each of the situations above and identifying similarities students then develop the concept of an angle. Furthermore, Skemp (1986) would say that this new mental object is at a higher level of complexity than each of the initial abstractions. We study the pieces, recognise the pattern and stand back and see the beautiful picture.
References:
Magina, S.M.P. (1994) Investigating the factors which influence the child’s conception of angle, Institute of Education, University of London.
Mitchelmore, M.C. (1998) 'Young Students’ Concepts of Turning and Angle', Cognition and Instruction 16, 265–284.
Skemp, R. (1986) The psychology of learning mathematics (2nd ed.), Harmondsworth, England: Penguin
SOMETHING TO TRY:
KS1: Use right angle checkers to identify right angles and angles smaller/larger than a right angle. Make checkers out of card and frames: such as straws stapled together. When using frames include L, ├ and ┼ frames
KS2: Order the angles below from smallest to largest.
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uoqDh8+HB/f//MzExB3JUS4MSyWCwURYuKio4dO2Zqaqqtrb1q1aqMjAwcx/PzsrOz16xZo6WlZW5u7uPjU1paSuSr7CCxXFdSUjJgwIDVq1fz4t8dw7Di4uJNmzapqanZ2dldu3atpaVF4LZZPYPEciA7O3v79u22trbS0tKzZ8++ffs2/28Y+xqTyczIyDh16pS7u7usrKydnd0ff/wRHR0tWJfgCHZi2Wg0WlFR0apVq5SVlQ0MDP755x9BvJ+PTqf7+voaGxsrKiquXLmypKSEUG+6/iZILNdlZWWpq6ufPXuWF+V7/vw5+1yXp6en8F26yQaJ/SEVFRVeXl76+vry8vITJkxISUlh3xWJ97j+H4PBqK6uTkxMnD59upKSkoaGhqur6507dwTlFT3CkFg2JpMZGRnJ/iLm4uKSnJwsKC8SoNPpqampbm5uUlJS/fv3Dw8PF5RtHySW66KioqSlpWNjY7n7es7W1lZ/f395eXltbW1/f39CbUO5CxLbG0wms6qq6tixY1paWnJyck5OTvfv3yf4d3oURdkPvlBVVe3Tp4+dnd3Vq1fr6upoNBqRj8QIT2LZampq9u7da21traWl5eXllZaWRuRcoSj69u3b/fv3GxoampmZbd68uby8HO9B/QBILNcdOnTIxMQkLS2NWzNkMpmvXr2aN2+ejIzM+PHj4+PjhfuJ35DYntFotOzs7JMnT9ra2qqpqY0bNy4wMLC1tRXvcf2A3NzcPXv2/PLLLwoKClZWVn/99dfjx48JuwjCllgWi8V+Ts0ff/xBIpFsbGwOHDhQUVFBwK85TU1NFy9eHDp0qLKy8oIFCxITEwVu3wISy3Vz5sxxdXUtLi7mytzodPr58+ft7Oz09fUPHDgg9O/mZEFie1RYWLhnzx4nJydpaempU6cGBwcL6DN8mExmYWFhcHDw3LlzNTQ0TExM5syZc/36dSKcQv6CECaWxWJhGNbW1vb06dNBgwbJyMgMHDgwNjYW70F9pqCgYPr06YqKirq6unfu3GlubibyZU3dgcRynZWVlaenZ2Nj48/PqrKycubMmYqKio6OjgkJCYJ1kQjHILHfVFdXt2fPHn19fTk5ueHDh8fFxRHtnCsH2PdfpKWlsZ/sqKSk5OjoePr0aUI9qEc4E9uJTqcfPXrUyMiI/fbNwsJCzg7c02i0xsbGqqqq0tLS9+/fl5aWVlZW1tbWtre3/1AaEQSpr6/38/NTUVFRVVVdtWpVc3Pzjw6GOCCx3NXS0iIpKbl+/fqPHz9WVFS8f//+/fv35eXl1dXVLS0tTCazl6sujUaLi4uzs7NTVFScPXt2ZWUlr0dOHJDYLzQ3N58/f97ExERBQcHW1jYoKIhQBeKWjx8/bt++3dTUVE5OTl1dff/+/e/fvyfCdwghTyyLxUIQJDU1dfny5To6OpaWlidOnCgrK+vl38UwrKamJioqat++fZMnTzY3N5eXl5eQkJCWltbR0RkyZMgff/wRFBTU+RbinrW1tYWHh48dO1ZeXn7ixIkRERGCckFWdyCx3BUXFyclJeXo6Dho0CB1dXX2Q9JVVFRsbW09PT39/PxSU1O/eya1rKxs//79enp6dnZ258+fJ/g1LFwHif1CUlKSlpaWm5vb2bNnGxoacBwJr6EoWlpaevr06YkTJ+rq6q5du5YIt5YIf2LZWltbIyMjp0yZoqqqOnLkyN58laPRaA8ePJg+fbq2traKisr48eO3bdt29uzZy5cvX7x4cf/+/YsWLbKwsCCRSEOGDDl48GDPD2B68+bNsmXLdHV1ra2tz507V15eLoinQL4AieWuffv2qaioTJw4cenSpUePHg0ICAgMDDx58uS6desGDRqkpKRkbW29fv36goKCb/51JpMZGxs7btw4eXl5T0/PV69eEeFbPJ9BYr/A3vSVlZUJ4qkoDmAYVl1dHRMTk56eToRtrKgklvXpBbQXLlwgk8nsB2++e/euu38DDMN27NhBIpFIJNKuXbuKioqam5upVCr7PXoIgtDp9La2tqqqquDgYCsrK2lp6VGjRmVlZX09QwqF4uvrq6urKycnt3Tp0oKCAqG5pBMSy13jxo2zsLDIyMhob29nMBgoiqIoymQyKRRKQ0NDYmLimDFjJCUlbW1t4+Pjv9hisu+r1tHRkZOTO3PmTGtrq4hsUr8Aif0ChmFEKA2fYRhGkPVfhBLbqaKiYsGCBWpqarq6uufOnauuru76ZZ99cHjWrFkyMjKTJ0/Ozc397gra0dGxe/duMplsa2v74sWLzumpVOrr168nT56soKDQr1+/0NBQIdurgMRyEZ1O19DQGDhwYA/HV1AUDQwMNDAwMDQ0fPToEXsjwmAwiouL58+fLysrO3To0NTUVD6OmnAgsYBQRDGxLBaLTqffvXt30qRJMjIybm5uISEhjY2N7MX8+PHjkiVLZGRkNm3aVFVV1csZMpnM27dv9+3b18bGJj09HUEQ9s1bOjo65ubmu3bt+vDhAy8XCB+QWC7Kzc2Vk5ObP39+z5Oxn5M+cOBAIyOjxMTE5ubmoKAgW1tbMpm8efPmkpISEdxl6QoSCwhFRBPLYrFQFC0vLw8ICOjfv7+Ghoanp2daWhqVSj127JiysvKOHTt+9FpfOp0eFhamqak5aNCgY8eOubi4yMjILFiwICUlBa+nafMaJJaL7ty5Iy0tfezYse9OyWQyExMTjY2NLS0tlyxZoqGhMWjQoPv37xP27nt+gsQCQhHdxLIhCPLhw4f169crKioqKSmtXbt2ypQpM2bM4GxrxWQyd+/eLSYm1qdPHwsLi8jIyI6ODiHeq4DEctHevXslJSXj4uJ6MzGCILt27RITE5ORkVm+fLmAPkCAFyCxgFBEPbFsCIJERUW5uLgoKSnZ2Njcvn37R3dhMQz78OHDyZMnyWSypqbm77//XlpaKvRbPUgstyAIMmfOHAkJie++F519weThw4dVVFSMjIxOnTollLc5cgwSCwgFEvv/GhsbT5486ezsrK6u/ttvvz1+/LiXD8Rpb28PDQ0dP348mUyeOnVqRESEiDxJBxLLLbW1ta6urmZmZj1/LUNR9OnTpx4eHurq6jNmzEhJSSHIZZPEAYkFhAKJ/QyDwXjz5s22bdvk5eXNzc3//PPPysrKHrZ6KIpmZGQsWrRIU1PT0tLy3Llzvb9CSghAYrklIyPDxsZmwYIFPUzT0tJy7NgxCwsLbW3tY8eOidSa1nuQWEAokNgvYRjGYDDevn3r6uoqISFhbm4eExPzzSkRBLl06ZKurq6YmNi8efMqKyvZd83yecA4gsRyS2RkpK6u7tmzZ7ub4MOHD3PmzJGWljY2Nn7x4kXvH6YoaiCxgFAgsd1qa2s7ffq0jY2NhITEggULXr16xb4wmP2OgWfPnk2aNElOTs7FxSU8PBzvweIDEssVGIZduHBBTk7u9evXX/+0tbU1Pj7e3t6eTCavXLmypaWF/yMUIJBYQCiQ2J6gKJqZmblp0yYjIyMLC4u9e/cWFRXl5eVt375dR0fHxMRk7969xcXFIrs/AYnlChqNtmPHDjU1tS/yiaJoQUHBtm3blJSUnJycrl692t7ejtcgBQUkFhAKJPb7qFRqUlLSrFmzlJWVnZyc7O3tVVRUlixZwr6PFu/R4QkSyxUNDQ1z58795ZdfvlidEhMTR4wYIScnt2zZspycHAaDgdcIBQgkFhAKJLZX2Cdor1+/vn79+oEDB969e5dOp4vszmsnSCxXlJeXDxo06Pfff+98Kw6KoidOnJCWliaTyVevXkVRFFa2XoLEAkKBxP4YDMNE7e1gPYDEckVubq6GhsapU6cQBGEwGOnp6TNnzuzTp4+bm9uTJ0/gtpwfAokFhAKJBZyDxHJFbGysvLz8gwcPqFTqhQsX7OzsDAwM9uzZU15ejvfQBA8kFhAKJBZwDhLLFceOHTM2Nr5x44aHh4eamtrQoUNjYmJE5OklXAeJBYQCiQWcg8Ryhaenp4qKiqKiori4+Lx582pra/EekQCDxAJCgcQCzkFiucLR0VFSUrJfv36XLl1iMpl4D0ewQWIBoUBiAecgsVzh7+/v7e396tUruLLp50FiAaFAYgHnILFcgSBIe3s73JbDFZBYQCiQWMA5SCwgGkgsIBRILPg+DMOYTAalve19UVnXQ5mQWMB/GIZROyjNTU0trW0o+uWuPyQW4IXJoFMoFCYT6fofIbHgO5o+FgRe9PM9e3bb1s3zfvuz6+oDiQV8VpaTEeB/4d/Ay4EBF7d5b/rn2OmC0squmYXEAv6jtjfcvh64f++By1eu/PPPvtNnrrUx/rczAokFPaG1fFgwa96jp6+SHt0eZGM4duHWrj+FxAI+Qp9HBS9bu/fhw7DZUz0uXAnLzU5b/uvQUTMX55Z+7JwIEgv4rKm8cO28yZNW7EjPzq+srHwVf81owGz6p+MrkFjQk4LksCnLNnS0Np3c/6dDX4vVf93q+lNILOAPDMMKs59v2nesvqW9qrTQfdSwe0kvMRar9O1rRz3dQ5dCkU9bNEgs4Cdae+OB9UsHjf2Nhnw6h8ZsXDB3U+cEkFjQk5YPReevht0P9t21d8+s6eOOhz3r+lNILOAPhEENv3ktKvEVirFynz9wHeb++m05i8Vqq6tcM3PEgj996Z9OgEFiAT9lv4i1t7e/n5zapZLMstLKzgkgseA78tMTZyxYl5X6bJrbqKj0wq4/gsQC/qC3N9257J+aW8VisW4c8Zo0b+XHVjqLxWqr//DHrJGr/r7AYP5vHwISC/gp9MzWYZM8iz40djcBJBb0hN5WM9vNyay//bixo9VNBmW9r+r6U0gs4A9GR4vfP1v2n7tFYzCXThm8bt9ZJoaxWKzKkhzXgXaB4YkoBgeKAQ4u7fScsnBtVROVxWIlhF1dssBzyvSFFW3/f1UoJBZ0i8mgXjnxl9+VaBRFU1OiR06dWfbxs8fnQmIBv2C5qUk7/v6nuvS1JVk3+P5zFoZR29vO7lrjPmNJyYeGzukgsYCfbvlsHDZ27tv3dRiGURor1y2cvPNcWNcJILHg21AE+S8mfPNfx6obWjEMiQq54OAy9GF03MfGjs5pILGAfzC09G3uiU2LtfRs7kQnP3xw/9TBvXNnLnyaWQA37QC8FGQ+HT3Eef2OvxMTE4MDTw0eMOxRSkbXCSCx4EsdzVVPnjx+GH5j9ar1L7LeoRiGYUhB7uvL14Lj4uMraimdU0JiAf9gaGl+zr3bwdeCbsXHx4fdvfsoNrG8y/4rGyQW8BOTTs14lnzG3//mrdtH/1rrPPzX3JKPXSeAxIIvVb55MWPaxPkr1qa/LUX+92B6jA1F0a4rAyQW8B/6yTef6gyJBXyGYRiTyWQwGD5bl67cdKiVBk93AlwCiQVEA4kF/NTWWHct4OLz19mVha9Hu42OTs3/YgJILOAcJBYQDSQW8FN7S8OZ4/vWb9nx9zbvkKhnyFcHViCxgHOQWEA0kFjAZ3RqR011dXNbxzd/CokFnIPEAqKBxAJCgcQCzkFiAdFAYgGh/GxiR44c6QtEFTETy62lO/0Jt2YI+MDKyopoibW3t8f7twJwc/z4cc4T29zcHAZEWGxsLNES+/jxY24tXfgn3Joh4A8URYmTWDqdjvfvA+Ds2bNn2dnZ7D+/ePHi6xWm28QqA5EnKytLnMRKS0tzcdGUPuHiPAF/ECexeP8mALEsWLDg6xWm28QC0IkIiQXgC7iskF0TC0BXP3agGIBOkFhAQLiskJBY0J3vJ7atre0RAF95+vQpHzdin3n58iUvlijqE17MHPAHLiskgiB4LzcgqPT09K9XGLFvPgsUAAAAAD8JEgsAAADwBCQWAAAA4AlILAAAAMATkFgAAACAJyCxAAAAAE9AYgEAAACegMQCAAAAPAGJBQAAAHgCEgsAAADwBCQWAAAA4AlILAAAAMATkFgAAACAJyCxAAAAAE9AYgEAAACegMQCAAAAPAGJBQAAAHgCEgsAANAmG9sAACAASURBVADwxGeJraqqWgHAV/bu3YvXCnry5EleLNHyT3gxc8AfuKyQNBoN7+UGBOXv7//1CvNZYvPz88UA+IqdnR0fN2KfcXd3x3vpAUHhskJSKBS8lxsQ1IwZM75eYSCx4PsgsYCAcFkhIbGgOz+W2CVA5A0ePJi9MhAhsfb29lxctKWfcHGegD86t1G4rJBdE4v3bwIQi5+f39crTLeJLSsrWwBE2JYtW/z9/YmT2D179hw4cIBbSzf/E27NEPAHgiDESWxbWxvevw+As+PHj1+/fp3951OnTn29wnSb2MzMzBUrVlQCUWVlZUW0xLq6unJr6T58wq0ZAj5wdXVlMpnESWxDQ8OECRPw/q0A3BQWFk6aNMnLy4uTA8WZmZkbN27k46oLiIWYicVrGIAI3N3diZbYb25VgYigUCiQWMAhSCwgGkgsIBRILOAcJBYQDSQWEAokFnAOEguIBhILCAUSCzgHiQVEA4kFhAKJBZyDxAKigcQCQoHECg8URV+8eNHa2sq3T4TEAqKBxAJCgcQKCQzDYmJiTE1NFy1axLcPhcQCooHEAkKBxAoDFEWTk5MtLCwsLCyePXvGt8+FxAKigcQCQoHECjwEQSIiIszNzW1tbaOiohAE4dtHQ2IB0UBiAaFAYgUbgiB37twxMTExNDSMjY2l0+n8/HRILCAaSCwgFEisAMMwLC4uztDQUFlZOTMzs+s/E39AYgHRQGIBoUBiBRWKoklJSZaWln379v3vv/9wGQMkFhANJJY4MAyrqKhgMpl4DwRPkFiBhCDIvXv3zMzM2Odf8VqJIbGAaCCxxJGWljZx4sQLFy4wGAy8x4IbSKzgQVE0NDTUxMRET08vPj6ez+dfu4LEAqKBxBJEfn6+u7u7uLj48uXL+XkNJtFAYgUMiqLx8fGGhoYqKipZWVn4DgYSC4gGEksE9fX1s2fPFhMTExcXLygowHs4eILEChIURRMSEiwtLfv16/fkyRO8hwOJBYQDicVdQ0PDmjVr2IsPgYDECgwEQe7evWtiYmJjY4Pj+deuILGAaCCx+GpoaPjjjz8kJSUlJSVNTU1LSkrwHhHOILGCAUXRu3fvmpqaamtrJyYmEuTyAUgsIBpILI7a2tq2bdsmIyNjaWkpJSW1b98+gmypcASJFQDs48PGxsYaGhrZ2dl4D+f/QWIB0UBi8UKn0/38/BQVFceMGTNmzBhra+v09HS8B4U/SCzRIQiSmJhoaWlpbW2dnJyM93A+A4kFRAOJxQWCIMHBwVpaWhMmTLh8+bK0tPSWLVtoNBre48IfJJbQEAQJDQ01Nja2traOiooi2lEXSCwgGkgs/6EoeuPGDR0dnZEjRyYlJbm4uBgaGmZkZOA9LkKAxBIXiqJhYWEmJibq6urJyclE6ysLEguIBxLLZxiG3bt3z8DAwNTUND09/eLFi/Ly8lu2bBHle2G7gsQSFIqiiYmJJiYm2trauN//2h1ILCAaSCw/YRj27Nkza2trMpmckZFRVVU1ZswYVVXVhoYGvIdGFJBYIkIQJD4+3sLCwsbGJjExEe/hdAsSC4gGEstPOTk5w4cPNzU1jY6ORhAkKCiITCafPHkS73ERCCSWcNjvpzM0NOzXrx8Bz792BYkFRAOJ5ZvCwsIRI0YYGBhcv36dTqc3NDSMHz/e2dm5qqoK76ERCCSWWFAUvXfvnomJiYqKytOnT4nwfIkeQGIB0UBi+aOysnLkyJFycnJnzpxhXzkcHh6uoKDg6+tL8K0Wn0FiCQTDsMTERFNTU319fULd/9odSCwgGkgsr2EYVlNT4+npKScnt2vXLnYdaDSajY3N4MGD8/Pz8R4gsUBiiQJBkLi4OEtLS1tb24SEBLyH0yuQWEA0kFhea2lp8fLykpWV9fLyYl82jGHY2bNnZWRkDh48CLuwX4DEEgKKouzzr3379o2Ojiby+deuILGAaCCxPEWn07ds2aKmpqalpdX5JJzS0lJra2tLS8v379/jOjoigsTiD0XRiIgIExMTZWXl//77T4C+BgpcYh8+fGhkZGT8icnnTLswMzPr/LP55yy+xfJzVl307aLf5/p3Yd2FTfdsu3B0dJwyZYqFhYW1tbWDg4OLi8vw4cPd3NwmTJjw66+/enh4zJ8/f+nSpatWrVq/fr23t/eOHTv27t176NCh48eP+/n5nT9/PjAw8Pr163fu3ImIiIiKikpISEhJSXn58mVGRkZeXl5RUVF5eXl1dXVTU1N7ezuTyey6KSAmSCzvIAiyc+dOGRkZDw+P3bt3X716lcViYRh26NAhWVlZX19fFEXxHiPhQGJxhmFYUlKSubm5kZFRZmYm3sP5MQKX2EePHpn2mtknpqamJjxj/BUDAwNdXd2uXwW6Y2Zm5u7uzp6JkZGRoaGhgYGBvr6+np6erq6ujo6Ojo6OlpaWpqampqamhoYGmUwmk8lqamqqqqokEolEIikrKyspKSkqKiooKMjLy8vJycnKysrIyEhLS/fp00dKSor9yhRxcXH2b1hCQkJGRkZJSUldXV1HR8fIyMjS0tLGxsbR0XHw4MGurq5ubm4TJ06cNm3a7NmzFyxYsGzZss7A//nnn3v37v3nn3+OHz/u6+vbGfjbt2/fu3fv0aNH8fHxT58+ffHixevXr3NzcwsKCoqKioqLi0tKSt6/f19aWlpWVlZWVlZRUVFZWfnhw4cPHz58nXxILI/QaLQzZ86QSKTBgwdXV1c/evRo8+bNGIa9e/du6NChVlZW8LjEb4LE4glBkOjoaAsLCzs7u7i4OOLvInxB4BKLYRj6OeRzzG4wukHvgtY9avc6uqBQKBQKJSYmZvv27a2trZRP2rtHpVLpdDqFQmlubq6vr6+urq6srHz//n1hYeHbt2/fvHmTkZGRmpr67NmzJ0+eJCYmBgUF7d+/Pzw8/O7duyEhIdevX7969eq///57/vx5Pz8/Hx+fY8eOHTp06O+//96zZ8+OHTu2bt3q5eW1bt26NWvW/P7778uWLVu8ePGCBQvmzZs3Z86cWbNmTZ8+ferUqZMnT54wYcK4cePc3NxGjRrl6uo6bNiwwYMHDxo0yNnZ2dHR0c7Oztraum/fvpaWlmZmZp3fJLS1tTU0NNTU1EgkkpKSkry8vIyMjJSUlISERGfRFRQUSCQSmUzW0tLS19c3NjY2Nzfv16+fra0tnU7/emWAxHId+xGJRkZGo0aNKi0tZbFYVVVV48ePz8rKOnXqlKqq6o0bN/AeI0FBYnGDoujt27fZ+wECdP61K4FLrEA4cuSIuLh4S0sL1+eMomhAQIC9vT2FQuF4DgwGg0ajUSiUtra25ubmxsbGurq6mpqajx8/VlZWlpeXl5aWFhcXsxufl5f35s2brKysjIyMtLS0V69evXjx4r///nvy5ElycnJCQkJcXFx0dPSjR48ePHhw//798PDw0NDQ27dv37p1Kzg4+OrVqwEBAefOnfPz8zt58uTRo0f/+eefffv27dq1a/v27d7e3l8/pQ8SywuxsbGmpqaurq6dTx5mXz4yf/58Y2NjFxcXuBe2O5BYfKAo+uDBAyMjIxKJ9PLlSwF9nicklhd8fX2lpaWLi4u5Pmc6nb57924VFZX29nauz5zrMAzrPOrQeYCh88gB+/AAHCjmg+fPn6uoqFhZWaWkpHQ928pkMg8ePKioqHj58mUB3YLxASQWB53nX9kPzsZ7OJyDxPJCcHCwqqrqvXv3uD7nlpaW5cuX29jYdHR0cH3mBAGJ5SIEQdLS0vr166ehoXH//v0vflpXV6elpTVmzJiysjJchicQILH8hiDIw4cP2edfY2NjBfoaPEgsLzx9+tTU1HT9+vVcn3NlZeWIESPmzp379SlMoQGJ5RYMw968eePm5qavr3/r1q0vDhggCLJjxw45Obnz588L3EUk/ASJ5Sv284fZ12vExsYK+pYOEssL1dXVgwcPNjAwoFKp3J1zenq6iorKqVOnhPiwHiSWWxobGydMmKCjo3P58uWvI5qVlWVqaurs7FxfX4/L8AQFJJZ/MAxj35dJIpHS0tKEYDMHieUFDMM2btwoJiYWFRXF3Tnv379fV1f3yZMnQrzbAYnlCgqF4urqqqSkdOLEia/vxmEymdu2bZOSkoqIiBDidYkrILF8wn7/K/vBBampqXgPhzsgsTzy/PlzWVnZ6dOnc/G6pPr6en19/enTp3/8+JFb8yQgSOxPwjCsrq5u0aJFUlJSmzdv/vricwzDXr9+bW9v7+bmBn39LkgsP7CvHzY3N7e3t4+NjRWC/Vc2SCyPIAji6empra0dFhbGlbP1DAZjw4YNKioqV65cEe7NIiT2JzU2Nm7dulVFRWXNmjXNzc1fT8BgMA4cOEAmk2NiYvg/PIEDieU59v2v7Mf1xcXFCeL9r92BxPJOWVmZsbGxu7s7+07/nxQaGqqiojJhwoTGxsafnxuRQWJ/0sGDB1VVVVevXv3NvrJYrMrKSmNj43nz5gn9usQVkFjewjAsJibG0NCQRCJlZmYK9PXDX4PE8g6GYUFBQTIyMuvWrfvJWWVlZTk6OiooKBQWFgr3LiwLEvtz/v33X0lJyZkzZ/ZwNmHr1q3q6uphYWFCvy5xBSSWh1AUTUpKsrCwsLKyevnyJd7D4T5ILE81NjauX79eRkZm9+7dHF+3mZOTM2HCBA0NDV7caEtAkFjOUKnUoKAgKSmpkSNH9vDO17dv38rLy0+dOhUuJO4lSCyvoCh67949MzMzOzu7mJgYoTn/2hUkltfKysqWL18uLi6+YsWK3NzcHzoKwmAwHj58OHz4cH19/QsXLgjTGYoeQGI5QKfT2S/TdHZ2fv36dXeT0Wi0ZcuWycnJhYWF8XN4Ag0SyxOd51+NjIwSEhKEdesGieWD6urqnTt3KioqDhw4MDg4uDeVxTCssrJy27Ztenp6enp6N27c4PihxAIHEsuBp0+fWlpaOjg45OTk9DBZUlKSvr7+uHHjRGd1+nmQWO7DMCwuLs7AwIBEIvW8ygo6SCx/YBh29+5dXV1d9u/54cOHPbw4rLW19cSJEzo6OmJiYs7OziUlJfwcKu4gsT+qurpaV1fX2Nj4+fPnPZxe7ejoWL16tYSEhHBv07hOeBJLpVIbGxtxv54IRdGEhARLS8v+/fs/e/YM38HwGiSWbzAMy8/PX7t2bd++fZWUlExMTBYtWnTs2LHbt29HRUVFRkYGBQXt3r17woQJioqKZDJ56NChfn5+Iri3AYntPRRF37x5079/f/ahjh5OZmEYlpKSYmpqumTJEn6OUAgISWIxDAsODl65cmVBQQGOw0AQJCwszNTUlH3+lclk4jgYPoDE8hmCIBkZGWfOnFm2bNmQIUP09PTk5OTExcUlJCSUlZUtLCzGjRvn5eV18+bNsrIy3L9u4gIS20sYhuXk5Li7uyspKQUEBPT8MFcmk7lhwwY9Pb3nz5/zbYTCQXgSe/36dXV1dTc3t9raWlzGgKJoaGiosbGxnp5eYmKisJ5/7QoSiwsURZubm4uLizMzM1+8eJGSkpKSkvLq1aucnJyKigohfotOb0Bie6m6unrmzJnKyspXrlzp4bwDW0FBgZqa2po1a1pbW/kzPKEhJIllsVh0Ov3o0aMKCgr9+/evqqri8z1bKIrGx8cbGhqSyeQ3b97w86NxBIkFRAOJ7Q0EQZYuXdqnT5/jx49/92YHFEVnzZplaGgYGxvLn+EJE+FJLIvFolKpBw4cUFZWHjNmTE5ODt8OlLH7amlpaW1t/fTpU/58KBFAYgHRQGK/q6GhYdOmTbKysps2bWpoaPju9I8fP5aQkFiwYAEXn5gtOoQqsSwWi0ajnTlzRltbe/z48Xl5eXz4RARB7t69a2JiYmtrKwrnX7uCxAKigcT2rKmpadeuXX369Fm+fHlVVdV3p29paZk2bZq8vHxKSgofhid8hC2xLBaLTqcHBARoaWm5uLhUVlZ+d/qKioqAgICVK1e6ubkNGjRo6NChM2fO3LVrV3x8/HcvyGSffzUxMdHW1n78+LEonH/tChILiAYS2wMajebj40MikTw8POrq6nrzV8LCwjQ1NZcuXSpqGzduEcLEslgsJpPp6+tLIpEsLCyKi4u/PmKMYRiNRktLS5s5c6aUlFSfPn3k5eUVFRWVlZWVlJQUFBRkZWWlpKTMzMzOnTvX1tb2zWPO7PtzTExMtLS0ROf8a1eQWEA0kNjuoCgaHh6uqKjo7u7ey6uWGhsb58+fr6SkVFNTw+vhCSvhTCyLxWIwGD4+PmQyefjw4V+///zdu3ebNm1SV1c3Nzf38PDw9/dPTU1taGhgMBgUCqWkpCQyMnLbtm2//PKLkpKSk5PTnTt3vnjvROf5VxsbmydPnvB34YgCEguIBhL7TUwmMyIiQl1dfcSIEdnZ2b25GpT9ChNtbe0dO3bwYYTCSmgTy2KxGAxGYGCggYHByJEjMzMzO/97YmLi8OHDNTQ01q5d+/jxYyqV+s2/jqJoaWnppUuXnJyc1NXVd+3a1fnkawRB7ty5Y2xsbGNjI2rnX7uCxAKigcR+DUGQ8PBwAwMDW1vblJSUXl4HiqLonDlz+vbtm5WVxesRCjFhTiyLxWIwGNevX9fV1bWxsSksLGSxWAkJCRYWFqqqqkFBQa2trd/9NocgSHl5+eLFixUUFDZv3sxisVAUDQsLMzY2VldXT0lJEeVTFJBYQDSQ2C9gGPbkyRNra2tNTc3U1NTev4/kv//+U1BQ2LFjR3c7IaA3hDyxLBYLQZBLly6RyWQTE5Pw8PChQ4cqKSnFx8f/0Ezq6+uXLVsmKSnp7+/PPv+qq6sLz+qExAKigcR+obi4eODAgZqamj/0YCY6nT5gwABLS0uhfAsnPwl/YlksFoIgFy9e1NHRUVRU1NHRuXHjBgczKSoqGjNmjIyMDPv9dMnJyVwfp8CBxAKigcR2VVRUNHr0aD09veDg4N6fz2I/j1ZMTGz9+vWifJSOK0QisSwWC0GQkJAQExMTAwMDzp7Oj6Lon3/+KSYmpqenFxoaCmseCxILiAcS26moqIj9WogzZ8780FMjPn78OHr0aBUVlXfv3vFueCJCVBLLYrGYTGZoaKiBgYGpqWl2dvYP/V329e7GxsaSkpKurq65ubk8GqRggcQCooHEsn38+HHu3LmSkpJHjx79ocdWYxh2+fJlEom0b98+0XyTBHeJUGJZLBaKokFBQVpaWoaGhs+fP+/lmX8MwxISEszMzAwNDb++/0eUQWIB0UBiWSxWS0vL5s2b5eXlt2/f/qN/t6qqasqUKcbGxnCVE1eIVmJZLBaKosHBwcbGxk5OTomJid/tJYIgMTExFhYWdnZ2SUlJfBmjwIDEAqKBxLa3t//999+qqqpr16794m7+3rh79y6ZTD516hQvxiaCRC6xLBYLRdH79+9bWVk5ODj0/OBNFEVv375tYGDQr1+/2NhYOP/6BUgsIBoRTyyVSt27d6+ioqKnp2d5efmPvnAMQZARI0a4uLjAWVhuEcXEslgsJpMZGRlpbGysra3d3bXsKIpGREQYGxuTSKSXL1+K7PMlegCJBUQjyollMpmnTp0ikUhDhgz5+PEjBy/0vHXrlry8/KFDh2Bzxy0imlgWi4Vh2N27d/X09PT19RMTE79YpdjnX83NzU1MTETz+cO9AYkFRCOyiWUymXfu3NHV1XVycurlI/6/0NTUZGhoaGdnl5+fz/XhiSzRTSyLxcIw7N69e1ZWVnZ2dlFRUZ3nZREEefTokYWFhb29fUJCAp/f7i5AILGAaEQ2sdHR0ebm5kOGDOFslwBF0ZMnT4qLix84cAAuJOYikU4si8XCMCw2NtbOzq5fv35xcXEsFgtF0ZCQECMjI0tLy7i4ODj/2gNILCAa0UxsfHy8iYmJjY1NcnIyZ7c8FBQUuLi4GBoaVldXc314okzUE8tisRAEiY+PNzc3V1ZWjo2NffDggZGREYlEgvtzvgsSC4hGBBObmppqaWmpqKgYFxfH2SYLQZDTp0/LyckFBQXBQTvugsT+T1RUlJGRkZycnK6urrm5eUZGBt4jEgCQWEA0opbY6urqGTNmkMnksLAwjmfy/v374cOHu7i4wFVOXAeJ/R8EQby9vcXFxR0dHRMSEuBsRG9AYgHRiFpi29vbAwMDb9269TMzuXjxopqaGuzC8gIk9n8KCgpu3rwZFhaWmpoK5197CRILiEbUEstisRgMxs/sErS1tfXt23fs2LHl5eVcHBVgg8T+D4IgLS0tGIbB97jeg8QCohHBxP6kQ4cOKSkp+fv7w6E7XoDEAs5BYgHRQGJ/yPv378lksouLS1VVFd5jEU6QWMA5SCwgGkhs7zEYjO3bt0tKSgYGBuI9FqEFiQWcg8QCooHE9t7r169tbW0HDRrU1taG91iEFiQWcA4SC4gGEttLDAZj//79kpKST58+xXsswgwSCzgHiQVEA4ntpbdv39ra2k6bNo1Go+E9FmGDYRiCICiKsSCxoDcYdFp11YeKysp26mf/b4TEAlxgn6AoSqfTuz7SCBLbS/v379fQ0Lh37x7cQ/GTMAxjMpmdt3qiDEr4rStHjh0LuHqrqbUdEgt60tFad/nCqXXrtvr4+Bz460+3KR6Jr4o6fwqJBXzWUPn28IHdcxfMnjh56saNGzf8sWrWwuX/Zb7t3EJBYnvJ19d33bp1tbW1eA9EoKH3Qq54b9k6a/Lk8TM30TAWi4VFXjpg7zIx8lHUpQsB1XWNkFjwbRiGtXws37lm+fnQ+Gt+exf9vi41/8OxjXNtp63r3GWAxAK+wTCsIv3JJNcxr98Wn/nba8GmoxQaE2NQIu6Hpb4p6JwMEgv4Bbvls2Hx35fa2urmjB629K9LLBaLUls0dIDt6Vv//7IjSCz4NoRBv3PV72b4IwaC3j+7ZezMJe8rq9d6Tl6040znNJBYwDf0trodu3dmv//YUlf124xxftciEBRrrG9E0M8eFwOJBfzCmO2s8DC1oiLnqYuj43/FjSwMS7gTaDNgbFOXJz1DYsG3tbc2Hv1rb3ULlcVCVk8aMOCXSZvXLO1v6ZZRVN85DSQW8M3HvFc7dx5saG6rLMoZ0M/qjy17rl79d8euM7TPH0kEiQX8gtw+vy/pZVHc7QATA5tzlwL8z/rOnjxm3roDXSeCxIJva20q37fzCMJiMdsr+2mo7vW5fuXcUV1d492+tzungcQCvql5+2qG+8zcirq0uCCnIe7345/nZiavW7cf/fxiHUgs4BuEyWDS2332eY2Z8Uda+uunsQ8nD3E5dye+6zSQWPBtbS11Kzzc41+9eZf8r5qGzpuqdgylzLY1HLl4R+c0kFjANxhCy36d0UqlnvSaO2/5llY6ymLfHcFkwoFigJfmjyXLJo86cysaw7Ci3Ndu4yakvM7vOgEkFnwbymTEh14PfxRzcN18uzGrqAhS/Dq5n6HxkX8fdU4DiQV8Rm+vdXM2P341EkVRDMOa6mpuXgupqGnunAASC/gCYzAYGIZlv4hzGzv+ZU4xxmL9F3XDfez0d6XVXaeDxIJutTY3hgcH2BhpjZ3x+6WL5zb8tnzXodNNlP9/0x8kFvBT6dvXB7YsV1LRmumxZP3mLT6+/hcunVvptb34Q1PnNJBYwAeMtjrfkyeiE19sXb9s94l/WykMFovls22584iJ/waFUbtcHwCJBd2i06hlJcWZmRnZb3Levn1bWFzS3gGPngC4aaipynidnp6R/Tot9cnj5JjYmMTkJ4VlHxjI/2/SILGAD1BmR3T4tX37D96LTm5qbWf/x7LC/NcZmXl575hdrg+AxALOQWIB0UBiAaFAYgHnILGAaCCxgFAgsYBzkFhANJBYQCiQWMA5SCwgGkgsIBRILOAcJBYQDSQWEAokFnAOEguIBhILCOVnE9u/f/+lQFQRM7HcWroln3BrhoAPdHV1iZZYIyMjvH8rADcLFy7kPLF0Ov09EGGVlZVES2xVVRW3lq70E27NEPAHhmHESSyCIHj/PgDOqqurGxoa2H+uqan5eoXpNrEAdCJCYgH4Ai4rZNfEAtDVj+3FAtAJEgsICJcVEhILugOJBRyCxAICwmWFhMSC7nw/sUwm8yMAX6mrq+PjRuwzDQ0NvFii6k94MXPAH7iskBiG4b3cgKAaGxu/XmE+SywAAAAAuAUSCwAAAPAEJBYAAADgCUgsAAAAwBOQWAAAAIAnILEAAAAAT0BiAQAAAJ6AxAIAAAA8AYkFAAAAeAISCwAAAPAEJBYAAADgCUgsAAAAwBOQWAAAAIAnILEAAAAAT0BiAQAAAJ6AxAIAAAA8AYkFAAAAeAISCwAAAPDEZ4ktKSlxAuArc+bMwWsFXbNmDS+WyPETXswc8AcuK2RHRwfeyw0Iytvb++sV5rPE5ufniwHwFTs7Oz5uxD7j7u6O99IDgsJlhaRQKHgvNyCoGTNmfL3CQGLB90FiAQHhskJCYkF3fiyxp4HI8/DwYK8MREjsuHHjuLhovp9wcZ6APzq3UbiskF0Ti/dvAhBLZGTk1ytMt4l9+/atNRBhkydP9vf3J05i9+zZs3jxYm4tXf9PuDVDwB9MJpM4iW1ubsb79wFwtnr16iNHjrD/vGHDhq9XmG4Tm5mZuXHjRj6uuoBYrKysiJZYV1dXvIYBiMDd3Z1QiW1oaPjmsUEgIigUyqRJk7y8vDg5UAyJFXGQWEA0kFhAKJBYwDlILCAaSCwgFEgs4BwkFhANJBYQCiQWcA4SC4gGEgsIBRILOAeJBUQDiQWEAokFnIPEAqKBxAJCgcQCzkFiAdFAYgGhQGIB5yCxgGggsYBQILGAc5BYwF0oira3t1dXVxcXF2dnZz9//jw+Pj4iIiI4OPjRo0dtbW3fnQMkFhAKJBZwDhILOECn06urq/Py8lJSUu7fv3/lypUTJ07s3Llz9erVc+bMxobc9wAAHN9JREFUmTJlypgxY3755RdHR8e+ffsaGhpqaGgoKiqOHDmyuLj4uzOHxAJCgcQCzkFiwTdhGNba2lpQUJCcnHzz5s2TJ096e3vPnz9/9OjR/fr109TUVFVVJZFIioqKCgoKsrKy0tLSkpKSEhISYmJiZDLZ1tZ27Nixixcv/vPPP319fe/cuZOSklJWVsZkMr/70ZBYQCiQWMA5SKzQQ1GUTqe3t7c3NzfX1dVVVVWVlZUVFRXl5+dnZ2c/fvz4zp07Z86c2b1798qVK6dNmzZkyBBTU1NFRUVxcfE+ffrIy8uTSCR1dXUdHR0DAwNTU1MrKysHB4cxY8Z4enpu2rTpyJEjgYGBDx8+TE1NraiooNPpPzlgSCwgFEgs4BwkVjgwmczm5ubKysr8/Py0tLTk5OTIyMhbt24FBAT4+Pjs27fPy8tr2bJlM2bMGD16tJOTk5mZGZlMlpKSkpaWVlNTMzQ07N+//6BBg0aNGjVlyhRPT8/ffvtt8+bNf//9t6+v79WrVyMiIpKTkzMzM0tLS5uamhAE4d2yQGIBoUBiAecgsQKEQqFUVFRkZGTEx8eHhIT4+/v//fffGzduXLhwYefpTycnp/79+5uYmOjo6KioqMjKykpJSZFIJFNT04EDB44fP37+/Pnr16/ft2/fmTNnbt68GRkZmZCQ8N9//71+/TovL6+kpOTjx4/Nzc00Gq3rRoOfILGAUCCxgHOQWEJBEKSuri4rKysqKiogIGD//v2rV6+eOnXqgAEDdHV1FRUV5eXl5eTkZGRkpKWlpaSk2Kc/2Ud09fT0Bg4cOG3atDVr1hw4cCAwMDA6Ojo7O7umpqa1tbW9vZ1CoXR0dNBoNAaDwWQyEQRBURTvJf4GSCwgFEgs4Bwklv9aW1vfvXsXGBh45MiRTZs2LVy4cNy4cQ4ODnp6ejIyMuwrhiQkJMhkso6OjpGRkbm5ef/+/R0cHIYNGzZ9+vSVK1fu3r3bz8/v1q1biYmJOTk5tbW1vbmMSFBAYvkDRdGGhoY3b95cu3Zt2bJljo6OampqkpKSkpKSqqqqjo6OK1asCAoKysnJaWxsJOa3Mf6AxALOQWL5rLW11dvbe+rUqZqamubm5g4ODsOHD584ceKcOXOWL1++cePGLVu2kEgkY2PjO3fuxMbGvnjxIi8v78OHDxQKBa8jt3wGieU1DMOamppCQ0MXL15sZGREIpEGDhw4c+bM1atXe3l5eXl5rVq1asaMGQMGDFBWVjYyMlq6dGlYWFhzc7OIrIFfgMQCzkFi+YlGo+3cuVNGRmbhwoUpKSnp6em5ublFRUWVlZX19fVtbW0MBqOwsFBXV3fChAl4DxY3kFhee/fu3bx58zQ1NXV1dbdu3RobG/v27dva2tqOjg4EQRAE6ejoqK2tzc/Pj4mJ8fb21tHR0dLS8vT0LCkpwXvsOBChxLLv1WtraxPNL1O8AInlGxRFL126RCKRnJycWlpauluHo6Oj1dTUtm3bxufhEQcklqdiYmKUlZVlZWVXrlxZW1uLomgPm1MMw1AUra6uXrFihaysrIqKSlxcHD9HSwRCnlgEQfLy8vz8/EaPHq2kpMQetrq6+uTJk//999+SkhKe3j8g9CCx/IFhWExMjLm5+YABA6qrq7ubDEXRgwcPysjIiOCGrBMklkc6OjquXLmirq5uZWUVHBz8Q3cwMxiMoKAgCwsLLS2ta9euUalU3o2TaIQ5sR0dHefOnXN2dpaTk3NwcPD09Fy/fv26des8PDz69esnKys7fPjwmzdvQmU5Bonlj+zsbEdHR3t7+2fPnvUwWW1t7a+//qqvr9/a2sq3sRENJJYXUBQNCQkxMjIaNWrUq1evOJvJ8+fPR4wYYWJicvfuXdE5lCi0ie3o6NiyZYuysrKpqam/v39+fn59fT2VSqVQKLW1tdnZ2UeOHNHV1dXQ0Dh27BhUljOQWD4oKSmxt7fX19e/e/cug8HobjIMw+Li4vT09LZu3crP4RENJJYXioqKzMzMfvnll4yMjJ+ZT1pa2uDBgy0sLETnvKxwJhZF0dOnTysoKBgaGubl5XU32ePHj8lksqqqakhIiOh8q+IiSCxPYRhWX1/v7u4uLi7u4+PT88QUCmX16tVkMrk3z8oXYpBYrmMymQMHDtTV1X348OHPzy0iIkJbW3vw4MHCdKtYD4QwsRiGZWZmOjg49NxXtqioKBUVlZEjR4rOtyougsTyVGNj48aNG0kkkre393cPtDx69EhFRWXLli0UCoU/wyMmSCx3oSh6/vx5CQkJb2/vHg6i9B6dTt+wYYOYmNiFCxdE4X5ZIUwsgiDHjx+Xk5MLCAj47sQYhu3atUtBQeHq1aui8O/NXZBYnjp8+LCGhsaaNWu+e3lIWlqapaXlwIEDs7KyRPx4DCSWuyoqKlxcXPT19UtLS7k1z/fv32traw8dOrSyspJb8yQsIUwsjUYbNWqUs7NzL3dM8/Ly9PX1lyxZ0tHRweuxCRlILO9cvXpVVVV11qxZFRUVPU/55s0bFxcXJSWlu3fvisjBtx5AYrkrODhYTU3t0KFDXPzqhmHYgQMH1NXVQ0JCuDVPwhLCxLa3tysrK69YsaKlpaU309fV1U2ePNnOzq6X04NOkFheQFE0Li5OQkLC3t4+Pz+/5ynfvHkzZMgQKSmpS5cu8W2ERAaJ5SIqlbpmzRpZWVmubxtbWlrk5OQ2btxIo9G4O2eiEcLEVldXi4mJ7dy5s5f/eK2trStWrNDW1m5sbOT12IQMJJbrEAR59uyZjY2NgYHB48ePu5sMw7Dq6uqbN2/279/f0NDw4sWL/BwkkUFiuaisrGzMmDETJ07kxczHjRs3duzY7x6kEXRCmNiamhoxMbEdO3b0kNjr16+XlJSwl6ulpWX58uW6urqQ2B8FieW6wsLCMWPGGBoaPnr06JsTYBhWU1MTFBQ0a9YsRUXF4cOH379/X+h3BXoPEstFGRkZ5ubm+/bt48XM9+zZY2FhkZ2dzYuZE4cQJra9vV1FRWXZsmXNzc3fnCAiIkJFRcXJyens2bNUKrWurm7ixImOjo5woPhHQWK5i8Fg/Prrr2Qy2cTEZM2aNSEhIXl5eS0tLUwms6mpKTc3NyQkZPXq1ba2tioqKhoaGgcPHiwvL4fzr11BYrnoyZMnysrKPDpjGhwcTCKRnj9/zouZE4cQJpZGo40ePdrR0bG7y50aGhqGDx8uKSkpJibWt29fX19fLS0tuNyJA5BYLqLRaMuXL5eRkVmxYsWwYcMUFBSkpaXZL6djk5CQkJaWVlBQMDU13bNnT21tLd5DJiJILBexrwlISEjgxcyjo6MlJCR6OBsiHIQwsQiC+Pj4yMrKXrhwobtpampqFixYIC8v37ksGzdu/PDhAz/HKQQgsdzS2tq6f/9+KSmpxYsX19XVtba2JiUlnT59euPGjQsWLJg1a9b8+fM3bNhw6tSpx48fi/LzEb8LEstFsbGxYmJiPKpgYmKiuLh4cnIyL2ZOHEKYWAzDcnJynJ2djY2Nu3ucJoZhFRUV69atk5aWlpKSIpPJ6urqEydODAwMrK+v5/OABRcklitoNNq///6rqak5depUUbhTkKcgsVyUlJQkKysbGRnJi5lHRETIycmlpKTwYubEIYSJZbFYTCbz4sWLJBLJ3Nz86dOn35yGfWvE1q1bxcXFra2tV61aRSaTlZSU2NePwFOLewMSyxWPHz/W09MbNmwYHEf5eZBYLnrx4oW2tra/v/8P/a1hw4ZZ9YKurq64uLihoWFvJhYUPj4+XzzCSDgTy2KxmEzmzp075eXlNTU1T5w4UVlZ2dra2tHRQaFQWlpaysrKdu7cSSKRNmzYcPr0aUVFxWHDhmVlZXl7e2tra0tJSY0ZM+bZs2dtbW3wyKceWEFifw6GYe/fvzc0NOzbt+/Lly9F/MFMXAGJ5aL8/HwnJ6eVK1f2/q/Mnz9fTExMpxe0tbU1NDS0tbV7M7GgOHz4sKgklsViIQhy6dKlAQMGyMrKGhsbe3h4rFu3bu3atVOnTtXW1lZQUBgxYkRERASVSj1//ryBgYG9vX1iYmJ6evrGjRv79eunpKS0cOHCyMhIuNK4O5DYn5SXl8d+wHpISAgcOOEKSCwX1dfXz5kzx8rKqvdvh2UntjdTdnR0lJeXC/39ZsKcWBaLhaJobm7umTNnPDw8rK2tNTU1tbW17ezsFi5c+O+//xYXF7O/cVAolJs3b2pra/fr1y80NLStre3ly5e7d+82MzPT1dX18PCIiIgQ8aerfxMk9meUlpbOmjWLfV2e0G9o+AYSy0UIghw+fFheXj4xMbGXf6X3iRURQp5YNgaD8X/t3XlUU2fewPEqO0ogKEtTECQqg1I8annFFzoHkIFRqwwigtXqWEV6pFJZahWVQfq2dZBK3VGHal06uKFUXittGU7FIlpQYJTSjMgqxIQ1kO0m98n8kWrxoiwhyXPJ/X3+8iTXmyeQky93fbq6ulpbW5uampqamvh8fnd3N2WjgSCI27dvOzk5qSfmJElSKpXW1NQkJCSYmJiw2ewlS5aUl5fjegv0BInVWE9PT3x8vKmp6eeffz70TQQwKEisdpWUlLi6uvr7+w/xkBkkloIRiR26u3fvenl52djYXLp06dn0JrW1tStXrpwwYYKZmdm6devu37/f29sLh81UkFhNEQRx6NAhc3Pz2NjYQWfRAcMCidUuhUKxcuVKExOTvLy8oXzpQWIpILHPIUmypKQkICDAwsIiIyOjvb1d/bhMJissLFy7dq2zs7Ojo2N8fPyPP/4IO/cgsRogCOLkyZPW1tZhYWF1dXW4h2NoILFad+/ePTs7uyFOqg2JpYDEUqlnL1m0aBGLxdq2bVvfy2S7u7uLioo2btzo4ODA5XLffffdmzdvamWa4lEKEjtcJEleuHDh1VdfnTNnDsztqguQWK1DCB09epTFYiUkJAx67icklgIS+wIIoa6urlWrVpmamsbGxvY9CIEQEovFZWVl4eHhY8aMmThxYnR0tMFPFvEykNhhQQjdunXL09NzwoQJv/zyC1wPpguQWF2QSqWxsbFmZmYZGRkDLwmJpYDEvlRbW1tMTIy5uXlUVBSfz++/wVFcXBwSEsJms9lsdmpq6sOHD6VSKaO2SyCxw1JfXx8UFOTg4GDwN43DCBKrI42NjeHh4cbGxjt37hQKhS/7AxESSwGJHQifz09KSjI1NQ0NDa2qqur/qRKJROfPn1+2bJmtra27u3tqamp5eTlztk4gsUMnEAiioqLs7e2PHTvG5IMLugaJ1Z1ff/111apV5ubm4eHhhYWFLzwZBRJLAYkdRGdn5759+9hs9vz58ysqKvovoJ6/Mz8/PyIigs1me3p6JiYmVldXMyG0kNgh6urqWrdunaWlZUpKCtzJRKcgsTrF5/MzMzOdnJzc3NzWr1/f/6xPSCwFJHZwCoXi9OnTbDbb3d29sbHxhcuQJCkWi7///vs33nhj7NixHA4nLS2tt7dXz0PVM0jsUMjl8h07dpiZmUVGRsKEiboGidU1hUJRWVm5ePFi9dSKXl5e27dvLygoaG5ulkgkb7/9NiS2L0jskKgvtHB2dra3ty8qKhrgXgEKheLMmTM+Pj5WVlZubm5ZWVn19fWGem8BSOyg1J8ce3v7oKAgg/+Tiw4gsfqhVCoLCwtXr17t7u7u4OAwbtw4IyOjKVOmTJ48GRLbFyR2qAiCOH/+PJfL5XK5OTk5A9wxACHU2tqalZUVEhIyfvx4Hx+fzMzMhw8f6nO0+gGJHdT169e5XG5AQEBtbS3usTACJFafSJJsamr69ttvDx48mJKS8tlnn/n6+kJi+4LEDoNSqSwtLfX29nZ2ds7Ozh54YZIkGxoacnJy/P39ra2t58yZs3v37paWFv0MVT8gsQP7+eefuVzu66+/XlxcDHf51w9ILF5wLJYCEjs86nkFfHx8jIyM9u/fP5Tle3p6zpw5w+Fwxo4dO2XKlFOnTikUCj0MVQ8gsQN49OjR9OnTrays8vLymHDuG01AYvGCxFJAYjVRVVUVGBhobGyckpLS1tY2lGthe3p60tPTZ86caWFhMW/evIsXLz5+/Hi0txYS+0IIoaampoiICGtr6wMHDuAeDrNAYvGCxFJAYjXE4/GioqLYbPbmzZufPHkylP9CkiSPx0tPT583b964ceMWLlyYnZ0tEAh0PVTdgcS+kFgs/uCDD+zs7D7++GPYP6xnkFi8ILEUkFjN8fn8uLg4Npu9YsWKoV/sSBAEj8c7cuSIp6cnm8329fU9ceKESCTS6VB1BBLbH0Jo165dbDY7Li6us7MT72AYCBKLFySWAhKrOYSQSCTavHmziYnJ3Llz+04YMCiSJDs6Oj799FNzc/MxY8Z4e3vfuHFj1N18ERLb3/Hjx1955ZWQkJDW1tZR9ws1AJBYvCCxFJDYkerp6dmyZQuLxQoKCqqsrBzujsHm5ubExMRp06ZZWlouXbr0u+++G+D+n3QDie2LIIi8vDxHR8eZM2dWV1fjGgbDQWLxgsRSQGK1QCqVfvHFF87Ozv7+/rdu3RrufycIoqysbPv27R4eHurdzhcuXBgVtwGCxD6DECopKZk1a9b06dPv3LmDZQxABYnFDRJLAYnVDrlcfvbsWRcXl2nTphUVFWmwBolE8uDBg7S0NPU9pIKDg69du0bz+8VDYp8RCAS+vr4uLi4FBQVYBgDUILF4QWIpILFagxC6cuWKnZ0di8W6evWqUqnU7FBcY2NjdHS0kZGRiYlJaGhoTU2NxqvSNUisSqVCCEkkkjfffJPFYh0/fhxOIcYLEosXJJYCEqtlBQUFHh4eLi4up06dGuAmi4O6e/fu2rVrXVxcbGxsYmNjb9682dXVRbfQQmJVKlVbW9uGDRuMjY2Tk5PFYrGeXx1QQGLxgsRSQGK1r7S0NCAgwNnZOTMzcyR7esVicWFh4aZNmxwdHZ2cnGJiYn744QdabSRBYkUiUVpampWVVUxMTEdHhz5fGrwQJBYvSCwFJFb7SJKsqqoKDg62trZOSkoayYlL6uuCKioq3nvvPVtb29deey0yMrKsrIwmpxwzPLEIodOnT9va2kZGRkJfaQISixcklgISqystLS1+fn5mZmZxcXEj38eLECovLw8ODjYzM7OysoqLi2tubiYIAu+uYyYnFiFUUVHBYrH8/Pzq6+v186JgUJBYvCCxFJBYHRIKhStWrLC1tY2NjdXKHDtKpTI/Pz8sLEy96zg1NZXH4418tRpjbGIRQqWlpRwOZ8aMGUVFRXQ7Rs5kkFi8ILEUkFjdEgqFiYmJEydOXL58+aNHj0a+QoRQR0fHlStX3nnnHQcHh6+//nrk69QYMxOr3n718/OztrbOzc0d7XM5GBhILF6QWApIrG6pi7hz504LCws/P78HDx5oZbUkSba3t1dWVuK9Cy4zE9vS0hIREWFhYXHx4kXoK91AYvGCxFJAYvWBJMndu3erp7GrqKgwmP2KDEwsQRBJSUmmpqZ79uzR6QsBzUBi8YLEUkBi9efYsWOTJk3y8fEpLi6mySnBI8S0xEokkvT09PHjx2/cuHFYsz4AvYHE4gWJpYDE6o9MJsvJyZk6daq7u/u5c+dodYWrZhiVWLlcfvDgQQsLi9DQ0Lq6Oh29ChghSCxekFgKSKxeEQRRVFTk4ODA4XC+/PLL0X4kjzmJJUkyNzfXyclp6tSpDQ0NBrOr3/BAYvGCxFJAYjGoqalxd3e3t7c/efKkXC7HPRzNMSex9+7d8/LycnV1bWxs1MX6gbZAYvGCxFJAYvGoqqoKCgqys7Pbu3dvV1cX7uFoiCGJraurCwwMnDx5cn5+Pmy/0hwkFi9ILAUkFg+SJO/fvx8aGmppaZmQkCAQCHCPSBNMSOzjx48XLlxoa2t79OjRUTGJL8NBYvGCxFJAYrFBCAkEgrCwMFNT0+joaKFQiHtEw2bwie3u7l6zZs2YMWN27Nghk8m0uGagI5BYvCCxFJBYzJRKZUxMjKWl5dq1a0ddZQ07sWKx+JNPPmGxWCtXrhztJ6YxByQWL0gsBSQWv/b29uTkZBsbmyVLllRVVY2io30GnFiE0IkTJzgczvLly/HeQgsMCyQWL0gsBSSWFtrb2zMyMoyNjf39/UtKSkZLZQ04sfn5+U5OTkFBQdXV1aPl1wFUkFjcILEUkFi6kMvlubm5lpaWXl5e5eXluIczJIaa2Nu3bzs4OLi6ut65c8cw7sPFHJBYvCCxFJBYesnNzZ00aRKXy719+zZBELiHMwjDSyxCqLq62tfXl81mX716VVsjBHoDicULEksBiaUXuVx++fLlGTNmODo6nj17luZXiRheYltaWqKiohwdHbOzs7U1PKBPkFi8ILEUkFjaIQiiuLjYw8ODw+EcPnyYLpVFZI+os6mpuUf6+7UrBpZYgiCio6MnTJiwe/duuESH5hBC6u8lhJBcKpFIf7tLGiQWL0isSqVCiFQ+vQYBEktHCKEnT554e3tbWloeOnQI93BUcqn4YOqHf/nL0m3bkmZPd8s4fE6OVCrDSixCaOvWraamphs2bOju7oZTnGhLJhZ9dSBt1pyZLBZrTsCflyx+6/VpLvuvVKqfhcTixeTEyns7zx7L8PaexfWau2f/kR4CqSCxtIUQ4vF4CxYsmDx5Mp/PxziS3k5B/OoFaxL/r7VTrFKpyq5/uX3vSfUHwpASq56eITg4uKWlRbvDA1pESLr/vvPDfSfyfrp00trG5RehTKVSXT6TxWvrVS8AicWLyYlVqVSd9RVzZ3qeKKp99ggklr4QQjU1NTdu3MA4BpKQ7E1eN+N/Fz168ttXGL+u7Ny1H9X/NqTEikSiAwcO8Hg87Y4NaNdPlw/Hb88mlMoDKbFeAdGEUiEUCISCDuXT7yhILF4MT2zptX/O9p7fQfx+GQIkFgyktuz7P7jaZ+Xfe/YIIRN3dP+WW0NKrEqlgutz6G9P8l+PXKpWiIWrw4LcvOZt/mBTYsqndU9EzxaAxOLF6MQi4qvPU5au2db3MUgsGAD5VeY2a/v/aZe/+MCkgSUW0N/+5HVB63c+/vdP/rM8r1XUtTTWnc/5Z6dU+WwBSCxeTE6svEf4YUzkx/+43PdBSCx4OUR88dH6P/xx2cueh8QCPZN0tJRX1Pzr6tez577V2inqvwAkFi8mJ7b5Pw8Wz//z/xff6/sgJBa8HCIyt8RwvBY824hVyHq7xQZ70Q4YFRTS3v07Ny1bv7VXIu//LCQWLyYn9u6N/MA/LariNfR9EBILBoAKvtpnZ/fqNz89UqlUpELy9y2xBfd+P70ZEgv0L+fw3zycJgYsiTp68Xr/ZyGxeDE1scpvDuz90x+93TznHs157q5wkFgwEKWsM/It//Est0/S976zNGLrnn/0fRYSC/RPJpUqSFIuk0plsBVLOw0NDZWVlbhHgYFE3KskkUJBiKXP3bUGEgsGQcol17+5mJV1vPhOFaFU9n0KEgvoBhILaAUSCzQHiQV0A4kFtAKJBZqDxAK6gcQCWhlpYt9//30xYCp6JlZb7673KW2tEOhBYGAg3RIbGhqK+6cCsBEKhZontra2dhFgsJiYGLol9qOPPtLWu3vrKW2tEOiHUqmkT2JFIhHunwfALDU1VcPExgPGCwwMpE9ifXx8tPjWNj+lxXUC/aBPYnH/JAAtzJ49W5PEAvAMHRILAAWWD2TfxALQFyQWaAgSC2gIywcSEgteZvDENjU1LQWgn/j4eD1+iT1n165dunhH4U/pYuVAP7B8IGUyGe73DWgqPT29/wfmucQCAAAAQFsgsQAAAIBOQGIBAAAAnYDEAgAAADoBiQUAAAB0AhILAAAA6MR/AUCff0Yl0AQEAAAAAElFTkSuQmCC)
KS3: What’s special about the angles in this triangle? Why do you know this?
![](data:image/png;base64,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)
KS4: The triangle below is folded as indicated. Explain how this shows that the internal angles add up to 180˚and that the area of a triangle is ½ base x perpendicular height.
![](data:image/png;base64,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)
KS5: What’s the difference between grad, rad and deg? Why would you need different systems? What are the benefits and restrictions of each system?
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