Similar Right Triangles within Right Triangles

OPTIONAL EXTRA CREDIT NOTES

If an altitude (perpendicular line) is drawn from a right angle to the hypotenuse, it makes three similar triangles.

If an altitude (perpendicular line) is drawn from a right angle to the hypotenuse, it makes three similar triangles.

If an altitude (perpendicular line) is drawn from a right angle to the hypotenuse, it makes three similar triangles.

If an altitude (perpendicular line) is drawn from a right angle to the hypotenuse, it makes three similar triangles.

Match the numbers to label new triangles.

64

36x

x

36

64

This triangle in not helpful, so we won’t use it.

36

100

x

x

64+ 36 = 100

Solve for x using proportions:

100 x . =x 36

The inverse of a square is a square-root.

36

100

x

x

100 x . =x 36

x2 = 3600

x2 = 3600

x = 60