Part A This is the start of an explanation of how to plan a coordinate proof that all equilateral triangles are similar. Choose the vertices necessary. Show that an equilateral triangle with side length a can be placed on the coordinate plane with these vertices. A. \( (0,0) ;(0, a) ;\left(-\frac{a \sqrt{3}}{2}, 0\right) \) B. \( (-a, 0) ;\left(-\frac{a}{2}, 0\right) ;\left(0,-\frac{a}{2}\right) \) C. \( \left(-\frac{a}{2}, 0\right) ;\left(\frac{a}{2}, 0\right) ;\left(0, \frac{a \sqrt{3}}{2}\right) \) D. \( (a, 0) ;\left(\frac{a \sqrt{3}}{2}, 0\right),\left(0, \frac{a}{2}\right) \) Part B Choose the words to finish the explanation of how to plan a coordinate proof that all equilateral triangles are similar. Show that an equilateral triangle with side length a can be placed on the coordinate plane with the vertices specified above. Similarly place an equilateral triangle with legs having length \( b \) on the coordinate plane. Show that there exists a \( \square \) that maps one triangle onto the other. Choose... reflection dilation Roviow Progress rotation translation Question 7 of 17 Back Next
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The correct choice of vertices for placing an equilateral triangle with side length \( a \) on the coordinate plane is A: \( (0,0); (0,a); \left(-\frac{a \sqrt{3}}{2},0\right) \). By using these specific coordinates, you're ensuring that the triangle's vertices lie on a neat, symmetrical position around the origin, making your proof more straightforward and visually intuitive. To finish your proof, you should choose “dilation” as the method of mapping one triangle onto the other. This technique allows you to show how the triangles, despite being different in size (one with side length \( a \) and the other with length \( b \)), maintain their shape – proving that they are indeed similar. Dilation is key in demonstrating the proportional relationships of corresponding sides.
