[math]3\cdot-8=(2\cdot-8)-8[/math]
[math]\frac{16}{-2}+\frac{24}{-2}=\frac{40}{-2}[/math]
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADIAAAAyCAYAAAAeP4ixAAAGtElEQVRoBc2aW2xURRjHv7PbXSjb2+422HuLFDWA9gIvaJQqGPAGCERCCEQefEC0CSQmAg+aiAQNBjVoRLTCiyQKLQaExBBDUJFSpd3dNkULFmhAS6/2btvdv/nmnLPnnO6Wru51k8l8c2Z25v+bby4nM4eKiorgdDqRkZGB9PT0BAj2CVpS76LJDofDgcLCQpDFYoHJZEJWVhby8/ORl5eH3NzcmAd9u2zn5OQgNzdf6MjLyQUH1iU/zxU62U5KSoLZbAbZ7XZR4MyZM2hqaoLb7RbB5XL5bfVZNOMGtwsuj1sEtZ1GN+tp8OvgfI/LDdbW5GlEfX09SktLkZqaCuLhVFBQgJaWFsTt59Na9kJO+HwceyHHnO/VCinW0NAQFi5cqIGwy7gX9D+uILYBmmgFrLOzEz9fOI/jx46i9tJP6Ovrg8IppHZ0dKCsrAw2m032CIN4PB49R1xt7sDLv7rxzLPLYLNJICKkppmwaeMG3Gi7KbT5fONgUB5aKSkpGgh7RHNjbDlYlPC+0my9qwHz5t8PomQQvQuJToPoNRCZsHbtanR3d4uSBhBedoMNrdiicGvyHGCg7du3CC8QHQTRAMg0KMe0Q6xQZ89+FwjCkz2uILqJzuP/n+FRLF++GBLZQdStAAwocS2IpuHol0cECM+RoEMr9l5QW9RWJK/Xi82bXxCCTdJFSOwREf4G0XFIZMLxmq8S0CMqi4hloJoTXyPDngqiRSDygKgHEp2HRMWYc98s/Nb8e2KCiC1DB8Re2bnzdaSlpUAiBioTcyYz04Hq6mp/ScNkj/scCbLR8cQfGRnF4SOfY+WKp7Fk6aNYtfI51FTLQ0olSTAQVRbv4qqtxD5gbGwMQyP9GB8f1e+FokBCgYj9w0+gTnqvYQefgOdPJhaIX5ZmCMf4vaPC6V5hINtdXV3RXn7lxlmLX4+mU3uDCJapKzeVGT2P+GTh6qtOgE4lPyjdVKqD5EcPRG1MJRCx3jvaMJGLTkyrFYQWRw9EAVA9oslRBKseUTJUXq3cf7OiBKKJZTkMc63lKo7WnMBHVYdxsbYuQGWCgmg6WeC3J08jp7gYGTYb0qdb4czKwr7978M7OiYXFBQJNrTknmVRsrBLv9Qhv2gWHkoy4Z3sDBwscGLVDCusFis+PnQI8IbrC7kvojK09PNi2eo1KDJJ8DxYiL/KZ6N9gRyWTLNgZmEh2tpuaO4Lw4oKiKqHgeY8vAiPT7cIAD1IpXOGOCg498OPcvEwHRNVEFZYWvEEypJMaF9QjD/LZ+POgmJhr0+dhmS7Uxw7qcNQ7YD/E0cBRJ4b7A3u5Lf27oWZCHuy03GlpAg3y+5FTfE9cJokVKxYBT7GicQvCiDKq4iP+9mH/sEBbKmshJkkPGA2ocxiRopEeHL5U2i9cT0SDKKOiIOoQ10crvGm5/NhcHBQrFAbKl/Bui1bsXvfe2hvbxcC9AtDOFQRB2ExenGqzbH/DT1AcXh7CFcXFZAAncoDFYqTwmb3qS6c7E8hPo8oiF7oZO0HKxMJliAg+QFnv1Mvj+EPjcnAQ30eBCQb7gaX/H99V/nt4KL92aG2HOFyBpBQj0z9wyPe6nWdYQCRj4OylaFl7HmjZjnPD6SrMF5mEBD5WsEoPNjqosKMx0u7od0AEL6z87gbDIWuXv0De95+Ey9v3YBt21/CiW+OGfLlPXzCoxgnA0FyjDdWra2tWFzxiLgkJUqCJJnhcGRg164d4gSQh1eA92IMwc3dFaS3rwfr168TlywS7QbRNRBdEAfKKTYrqqo+UySHdogWTb4AEP39iNtzGXa7FUTbJtxNuEDkxJNLKzA8PBxNfSHXHRREvUOsrT0Hi5Xv7U6BJOVuQhqAZOqHRMswb/4c3LrVJjcW4/E1ccVkEL4MNdwh8t01/xob3ch0sEdehUR9kCTl2ku6AiIHlgiPDBpeEkPuwggU1MNM4pEm0Uxvby82vbhR3EdI0hsgugSi72Gix2C1mPHJwQMRkBN+FQwUAMKfQoh7dmWo3LzehrVrnodEBBNlgleunNyZ+ODDAxgdMW6a4Uuauga9F/SlJwdRSjFPT08PTp6qwf79u1H1xafwNNYD48qZlL62ONoBIPwxTXNzs0GSfh6rtognHFQb/hSDhN47/f39KC8vlyc7vzQySF1dnfACU3Lo6rwjYjXdqUt3dXRPyJP/o5WNfJrvQvT180cDt2/f1r5FsVqt4E+d5s6dK+j43jpRAy+1qja2S0pKkJycLD51In7P4jdgXos58AcqHNR0osdpaWnig4d/AURmCJ8E3o4HAAAAAElFTkSuQmCC[/img]
Rotate triangle [math]ABC[/math] [math]180°[/math] around the midpoint of side [math]AC[/math]. Right click on the point and select Rename to label the new vertex [math]D[/math].[br][br]Rotate triangle [math]ABC[/math] [math]180°[/math] around the midpoint of side [math]AB[/math]. Right click on the point and select Rename to label the new vertex [math]E[/math].[br][br]Look at angles [math]EAB[/math], [math]BAC[/math], and [math]CAD[/math]. Without measuring, write what you think is the sum of the measures of these angles. Explain or show your reasoning.
Is the measure of angle [math]EAB[/math] equal to the measure of any angle in triangle [math]ABC[/math]? If so, which one? If not, how do you know?
Is the measure of angle [math]CAD[/math] equal to the measure of any angle in triangle [math]ABC[/math]? If so, which one? If not, how do you know?
What is the sum of the measures of angles [math]ABC[/math], [math]BAC[/math], and [math]ACB[/math]?
What is [math]m\angle DBA+b+m\angle CBE[/math]? Explain how you know.
[size=150][size=100]Use your answer to explain why [math]a+b+c=180.[/math][/size][/size]
Explain why your argument will work for [i]any[/i] triangle: that is, explain why the sum of the angle measures in [i]any[/i] triangle is [math]180°[/math].
What is the sum of these four angle measures?
Come up with an explanation for why anything you notice must be true (hint: draw one diagonal in each quadrilateral).