Spring Break Starts at the end of Today! Complete this warm-up as an exit ticket to turn in. A playground has a slide, a swing and a sandbox. The slide and the swing are 32 feet apart, the swing and the sandbox are 50 feet apart, and the slide and sandbox are 48 feet apart. Do the three pieces of apparatus form a right triangle?

Today’s Plans Exit Ticket as Warm-Up Using Similarity with Right Triangles Similar Right Triangles Notes

CC.9-12.G.SRT.4- Prove theorems about triangles. CC.9-12.G.SRT.5- Use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures. CC.9-12.G.MG.1- Use geometric shapes, their measures and their properties to describe objects. Apply similar right triangles!

Using Similar Right Triangles

What’d You Learn? How are the two smaller right triangles related to the large right triangle? How would you show that the green triangle is similar to the red triangle? How would you show that the red triangle is similar to the blue triangle? What were some proportions that you created using the geometric mean?

Theorem 7.5 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and each other.

Example 1 Identify the similar right triangles in the diagram. TSU ~ RTU ~ RST

Finding the length of an altitude to the hypotenuse. Swimming Pool The diagram below shows a cross-section of a swimming pool. What is the maximum depth of the pool?

Using a Geometric Mean Find the value of y. Write your answer in simplest radical form.

Geometric Mean (Altitude) Theorem In a right triangle the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the two segments.

Geometric Mean (Leg) Theorem In a right triangle, the altitude from the right angle to they hypotenuse divides the hypotenuse into two segments. The length of each leg of the right triangle is the geometric mean of the segment of the hypotenuse that is adjacent to the leg.

Solve! Rock Climbing Wall To find the cost of installing a rock wall in your school gymnasium, you need to find the height of the gym wall. You use a cardboard square to line up the top and bottom of the gym wall. Your friend measures the vertical distance from the ground to your eye and the distance from you to the gym wall. Approximate the height of the gym wall.