8.5+(winbr5)

Proportional Altitudes Theorem
If two triangles are similar, then their corresponding altitudes have the same ratio as their corresponding sides.

Proportional Medians Theorem
If two triangles are similar, then their corresponding medians have the same ratio as their corresponding sides

Proportional Angle Bisectors Theorem
If two triangles are similar, then their corresponding angle bisectors angle bisectors have the same ratio as the corresponding sides

Proportional Segments Theorem
An angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides

Examples
//this picture is an example of the angle with the girls ball and the angle from the hoop to the ground.//

AB/DE equals BC / EC there fore x/20 equals 36/15, or x/40 equals 12/5 x=12/5 × 20 = 48 meters
 * Similar triangles to measure Distances**

Because angle ABE is congruent to ACD and angle A is congruent to angle a, triangle ABE is simular to triangle ACD by AA similarity, and so AB/AC = BE / CD therefore: x/x+32 equals 60/80, or x/x+32 = 3/4 4x=3x+96 -3x -3x x=96 meters
 * Simular Triangles to measure Distance**

Both the girl and the basketball hoop are perpendicular to the ground, so the two triangles are similar by AA Similarity Postulate. x/35 = 42.5/ 25 35 × x/35 equals 42.5 / 25 ×35 x= 59.5 inches the hoop is one inch below regulation height.
 * Find Height of a Basketball hoop**

x/12 = 16/20 12 × x/12 = 16/20 × 12 x=9.6
 * Triangles are similar solve for x**

Triangles are similar solve for x 2/3 = 1.6/x __2x__=__9.6__ 2x 2x x=4.8