Pearson Geometry 7.4.notebook
March 16, 2017
Similarity in Right Triangles
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.
IF... ΔABC is a right triangle with right angle ACB,
and CD is the altitude to the hypotenuse.
THEN...
**Notice the corresponding angles in each triangle.
What similarity statement can you write relating the three triangles in the diagram?
1
Pearson Geometry 7.4.notebook
March 16, 2017
Geometric Mean ­ For any two positive numbers a and b, the geometric mean is the positive number x such that What is the geometric mean of 6 and 15?
What is the geometric mean of 4 and 18?
2
Pearson Geometry 7.4.notebook
March 16, 2017
Corollary 1 to Theorem 7.3 ­ The length of the altitude to the hypotenuse of a right triangle is the geometric mean to the lengths of the segments of the hypotenuse.
IF....
THEN....
Find x.
Find y.
3
Pearson Geometry 7.4.notebook
March 16, 2017
Corollary 2 to Theorem 7.3 ­ 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 hypotenuse and the length of the segment of the hypotenuse adjacent (next to) to the leg.
IF....
THEN....
Find a and b.
4
Pearson Geometry 7.4.notebook
March 16, 2017
Find x, y, and z.
Find x, y, and z.
5
Pearson Geometry 7.4.notebook
March 16, 2017
Find x and y.
6
Pearson Geometry 7.4.notebook
March 16, 2017
P. 465 9 ­ 21, 24 ­ 28, 38 ­ 41 7