IM Geo.1.7 Lesson: Construction Techniques 5: Squares

Which one doesn’t belong?
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[/img][/td][td][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAACLCAYAAAByQjsqAAALhUlEQVR4Ae2dV2gVTxvGg4hdFEQN9gY2NBZUxI4lXqjYu6gIxoZ6IWIvUcGKXcQLIxoVBRXsLVgvVKwXasQuKtiwx3Yxf575WL8kbpndPXvOnN1nIJyT3Xfa8/7O7O7slBTBQAUCViAl4PSZPBUQhIwQBK4AIQtcYmZAyMhA4AoQssAlZgaEjAwErgAhC1xiZvAPZLm5uSItLU2kpKT885ednU3FqIBrBSwhKwyUAR8AxHcGKqCqgDJkSDAvL09kZGSI9PR08f79e9U8aBdxBVxBBq2MFq1wSxdxHVl9GwVcQ4YWDC1ZZmamTbI8RQX+r4BryIxLJi6b+M5ABZwUIGROCvG8bwVcQ8bLpW/NI5eAa8guX74s+8/wyUAFVBRwBZnRivF+TEVa2hgKKENmtGAEzJCOn6oKWEJW+LUSO2BVJaVdYQX+gaywAf+nAn4VIGR+FWR8RwUImaNENPCrACHzqyDjOypAyBwlooFfBQiZXwUZ31EBQuYoEQ38KkDI/CrI+I4KEDJHiWjgVwFC5ldBxndUgJA5SkQDvwoQMr8KMr6jAoTMUSIa+FWAkPlVkPEdFSBkjhLRwK8ChMyvgozvqAAhc5SIBn4VIGR+FWR8RwUImaNENPCrACHzqyDjOypAyBwliq/B06dPRd++fUVWVlZ8Mw4wN0KmKO6hQ4cCdzzyKF++vChXrpxYuHChYsn0NyNkCj6aNm2anDXfqVMnBWtvJmvXrpVwoQVDPoTMm45JF+vjx4+iWbNmcnlTgBYkZOfOnRO3bt2SGtWsWZOQJR0tHgsMyAAXPtGyBAlZ/iJiYjVbsvyKROQ7IfPuaN6TKWpHyBSFMjEjZCaimB0iZGaqqB0jZGo68Z5MUSczM0JmporJMbZkJqIoHiJkikL5gez8+fOKufzPjE+XruQKj7FbyF6+fCkWL14s0OfVvn17Ua1aNbFgwQLx7NkzR1EImaNE4TRQhSwnJ0cMHz78775UAwcOFEuXLhVDhgz5ewzfT58+bSkUOmbxDjMsgZdLRU/C6UaPfOEoP3/+FFu2bBEtW7aUIKWmpoq5c+eKx48fFzBFK4bWDK0aWiu8Tdi4caP4/v17Abuw/UPIfHj0zp078o1A2bJlJTR4I7Bz506lFHfv3i26du0q45UqVUpMmTJF3Lx5UylushkRMg8e279/v+jZs6cEpGjRomL8+PHi6tWrHlIS4vr162LSpEmiePHiMr3u3buLvXv3ekpL10iETNEzr169EkuWLBG1a9eWMDRu3FisWbNGfPr0STEFe7OvX7+K9evXi6ZNm8r0a9SoIRYtWiRevHhhHzEJzhIyByfhJnzUqFHS8biP6t+/vzh69KhDLH+nT548KQYNGvQ3z2HDhokzZ874SzSBsQmZifi/f/8WW7duFa1bt5aOrly5spg9e7Z4+PChiXVwh/CwMW/ePFGlShVZDjxYbNq0ydXGaRgIiRYxkYGQmag/ceJEeVns2LGj2LFjh4lF/A/t2rVLdOnSRVStWlWMHTtWqQDodkHri79EhsTmnsiaW+T97ds3UaJECTF48GALi8QeNi7ddjsnY/xb586d5WBLjLglZAH7DIMOIbhqQL8VnGLVJ6aaTlB29+7dk+VbtWqVbRZoxQAb7ikJma1U3k9CYHR2YlKGG5FbtGghunXr5j3jOMTs1auXaNSokVJOhExJJvdGuGHGrJ/Ro0fLGUaqkJ09e1YCiY5SncOBAwdkOY8dO+ZYTELmKJF3AzxVIRg3vyopjRgxQj7Jqdgm2qZOnToC70WdAiFzUigG51Uhe/36tWwd8M4xGQI6htFCO71IJ2Rx8KYqZMuWLZNOe/ToURxK5T8LDCUCZHjhbhcImZ06MTqnClm9evVEv379YpRrfJLBmwCM6LALhMxOnRidU4EM929oFQ4fPhyjXOOTDMakodx2L9QJWRx8oQJZnz59RP369eNQmthnkZaWJnr06GGZMCGzlCZ2J5wge/DggWwNli9fHrtM45jSunXrZPkxts0sGB2yZufidSz0r5WcIJs1a5Z00ps3b+KleUzz+fz5syhWrJiYPn16TNONZWKRhwwjLNBpm8whIyNDvtn48+ePltUIPWR2qmOoNG6c3U5Zs0szEeeuXLki67Ft27ZEZO+YZ6Qhw9CZVq1aOYqUDAYdOnQQbdu21bKokYUMY+vRimGWURjC9u3bZX0uXbqkXXUiC9nkyZNF6dKlxY8fP7RzitcCVahQQYwbN85r9MDiRRIyzHM0pqEFpmwCEp4xY4YoUqSI+PDhQwJyt84ykpBt3rxZXlpu3LhhrUwSnrl7966s1+rVq7UqfSQh0330q1dC7t+/LyFzGjXrNX2v8SIJmTGOf+rUqV510zLezJkzJWR24/8TUfBIQgahMSMJywtgHYuwhIoVKyrPZIpnnSML2bVr1+SvHvMrwxAwdQ9dMhcvXtSuOpGFDJ7AAilt2rTRzileCqRzXSINmfHrv3Dhghe/ahMHi72gFdO1VY40ZKCkUqVKWt7HuCHYuL/89euXaTRM8MXc00TNJY08ZMYT2bt370wdpPtBrAaEGe9mT8oYSzZmzBg5kxwtHQYwJiJEHjKjb2nlypWJ0N93nhs2bJCXSrNWCvdpGDkL2AiZb6mtE4DA2D8SIluF3r17i4YNG1qd1vp48+bNLWe852+5CFlAbsSvu1atWn8vF1bZHDx4UEIY9LpjVvl7Pe5mxjsh86qyTTy0YMaWfiqTKerWrSsGDBhgk6J+pzDjHUtJqQRCpqKSBxtjdrUKZFgGHY548uSJh5ziH8WY8Y5F8lQCIVNRyYeNCmRYExaOmD9/vo+c4hfVmPFeeBl3qxIQMitlYnRcBTJkhU0enGZkx6hIvpPBjHesX6saCJmqUh7tVCHD4r9wht2MbI9FiGk040HlyJEjyukSMmWpvBmqQobUsXCe3YxsbyWIbSzMeG/QoIGrRAmZK7ncG7uBDGvpwyFWM7Ld5x7bGLm5ubJ8K1ascJUwIXMll3tjN5B9+fJFzsjG/ZmOAa+JAMzbt291LJ5pmay7wU3Nk/OgG8hQQ8zIRicu5mVmZ2drUWncJ2JLHDyYJNuM90hAhp5/vMdTDXl5eXJTBixSjFYDmzWga8Pod1NNx68dtrzBRg/YAgflwJY4WGAFL8WTKUQCMj8OwRMnFpuDk/GH9f2xLU2QAa+L8ueJLXBOnDgRZJaBpk3IFOU1WpXq1atL2DC6AQ8JsWpVMMkYU/WMPTPReqI3P1neQNjJSMjs1LE4t2fPHjnyAS0bxnJhK0Ese+Al3L59W44FK1OmjIQX94HY4iZMgZD58CYmB2O5g5IlS0pAsEmq6h4A+/btE+np6TIe1hebMGGCwOSWMAZCFgOvYh4nBg+iIxetGy6pWHzv+fPnBVLHitWZmZnyyRV2TZo0ERgajYXswhwIWYy9e+rUqQKb2g8dOlRg1O3IkSMlgIALQ4qOHz9um7MxdBr26IJJ5kDIXHrPGAjp1CVibGqP8V7t2rUTqampYs6cOUJl1ATyQKuIPAiZSwclu3lWVpbcswlPlk6Q5a9rTk5O/n8dvyNto8OVkDnKFR4DAIYd57DmP7Y3dAOZWxVwqTQCITOUiMgnLmMIACxIyPLLScjyqxGh74TMnbN54+9OL2lNyNyJRsjc6UXIPOhFyDyIxpbMnWiEzJ1e0pqQuRONkLnTi5B50IuQeRAtni0Z8jK6TjwUVYsohMyDG+IJmYfiaReFkGnnkvAViJCFz6fa1YiQaeeS8BWIkIXPp9rViJBp55LwFYiQhc+n2tWIkGnnkvAViJCFz6fa1YiQaeeS8BWIkIXPp9rViJBp55LwFYiQhc+n2tWIkGnnkvAViJCFz6fa1YiQaeeS8BWIkIXPp9rViJBp55LwFYiQhc+n2tWIkGnnkvAViJCFz6fa1YiQaeeS8BXoPzYe6j+wS6ncAAAAAElFTkSuQmCC[/img][/td][/tr][/table]
Use straightedge and compass tools to construct a square with segment AB as one of the sides.
Here is square ABCD with diagonal BD drawn:
[list][*]Construct a circle centered at [math]A[/math] with radius [math]AD[/math].[/*][*]Construct a circle centered at [math]C[/math] with radius [math]CD[/math].[br][/*][*]Draw the diagonal [math]AC[/math] and write a conjecture about the relationship between the diagonals[math]BD[/math] and [math]AC[/math].[br][/*][*]Label the intersection of the diagonals as point [math]E[/math] and construct a circle centered at [math]E[/math] with radius [math]EB[/math].[br][/*][/list][br]How are the diagonals related to this circle?
Use your conjecture and straightedge and compass tools to construct a square inscribed in a circle.
Use straightedge and compass moves to construct a square that fits perfectly outside the circle, so that the circle is inscribed in the square.
How do the areas of these 2 squares compare?
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Information: IM Geo.1.7 Lesson: Construction Techniques 5: Squares