1. “What we do in life echoes in eternity.”

2. 7.4 Similarity in Right Triangles

3. Similarity in Right Triangles Theorem 7-3: The altitude to the hypotenuse of a right triangle divides the triangles into two triangles that are similar to the original triangle and to each other.

4. Geometric Mean Geometric Mean: The number x such that, where a, b, and x are positive numbers Find the geometric mean of 3 and 27. Review: How do we find the arithmetic mean of 3 and 27? Note: Find the geometric mean of 4 and 18.

5. Geometric Mean 5.2 in8.75in 6.75in Corollary to Theorem 7-3: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse

6. Proof of Corollary to Theorem 7-3 A C D B StatementsReasons 1. 2. 3. 1. 2. 3. Altitude of rt. Δ to hypotenuse divides into 2 ~ Δs

7. Similarity in Right Triangles Find the values of x and y in the following right triangle.

8. You Try One!!! Find the values of x and y in the following right triangle.

9. “You wasted $150,000 on an education you coulda got for $1.50 in late fees at the public library.”

10. 7.4 Similarity in Right Triangles HW 7.4: #1-21, 34, 35, 50, 51

11. Real World Connection As Marla arrives at the lake from the parking lot, she reads a sign that says she is 320m from the dock. How far is Marla from the information center?

12. Kick it up a notch! Find the value of x in the following right triangle. x1 2x - 1

13. Similarity in Right Triangles