Transcript Special Right Triangles

Refresh Your Skills for Chapter 12

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

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:

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.

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