1. Refresh Your Skills for Chapter 12

2.  If you split an equilateral triangle in half along an altitude, you create two right triangles with angles of 30°, 60°, and 90°. If the original triangle has sides of length 2, you can use the Pythagorean Theorem to find the length of the altitude, which is the longer leg of each new triangle. You can use the side length relationships of this 30°-60°-90° triangle to find the side lengths of similar

3.  The unmarked angle of the triangle measures 30 because the sum of the angles of any triangle is 180°. All 30°-60°-90° triangles are similar, so you can use the comparison triangle and write the following proportions:

4.  You can make another comparison triangle by cutting a square in half along the diagonal to form two isosceles right triangles. You can use the Pythagorean Theorem to find the length of the hypotenuse.

5.  The hash marks indicate that the legs are equal in length, so a 9. You can then use the isosceles right comparison triangle to write the proportion