OBJECTIVES: 1) TO FIND AND USE RELATIONSHIPS IN SIMILAR RIGHT TRIANGLES. PDN: PG.439 #2-8 EVENS 8-4 Similarity in Right Triangles M11.C A

THEOREM The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

Vocab For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that:

Example: Find the Geometric Mean Geometric mean of 3 and 12

Check Understanding Pg. 440 #1

Corollary to Theorem (1) The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments to the hypotenuse

Corollary to Theorem (2) The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.

Example: Apply Corollaries 1 and 2 Solve for x and y

Check Understanding Pg. 441 #2

Example: Real-World Connection At a golf course, Maria drove her ball 192 yards straight toward the cup. Her brother Gabriel drove his ball straight 240 yards, but not toward the cup. Find x and y, their remaining distances.