Geometry Chapter 7: Right Triangles and Trigonometry 7.3-­‐ Use Similar Right Triangles SWBAT: use properties of the altitude of a right triangle. Common Core: G.SRT.8; G.SRT.6
“Do Now”
a) Find the geometric mean of 42 and 24
b) Solve the proportion
Theorem 7.5
If the altitude is drawn to the hypotenuse of a right triangle, then the two
triangles formed are __________________ to the original triangle and to
each other.
∆𝐶𝐵𝐷 ______ ∆𝐴𝐵𝐶, ∆𝐴𝐶𝐷 ______ ∆𝐴𝐵𝐶, and ∆𝐶𝐵𝐷 ______ ∆𝐴𝐶𝐷
Example 1: Identify the similar triangles in the diagram. (Hint: Draw the triangles in the same orientation) a) b) !
!
!
=!
Geometry Chapter 7: Right Triangles and Trigonometry Example 2: A cross section of a group of seats at a stadium shows a drainage pipe 𝐵𝐷 that leads from the seats to the inside of the stadium. What is the length of the pipe? Example 3: Find the value of x. Example 4: Find the value of y leaving your answer in simplest radical form. Does this proportion remind you of anything you’ve seen in the past? Geometry Chapter 7: Right Triangles and Trigonometry v Think EKG Machine used in hospitals Example 5: To find the clearance under an overpass, you need to find the height of a concrete support beam. You use a cardboard square to line up the top and bottom of the beam. Your friend measures the vertical distance from the ground to your eye and the distance from you to the beam. Approximate the height of the beam. Example 6: Find the value of y. Write your answer in simplest radical form. Practice: 1. Find the value of a. Write your answer in simplest radical form. Geometry Chapter 7: Right Triangles and Trigonometry Write a similarity statement for the three similar triangles in the diagram. Then complete the proportion. 2. 3. Solve for the variable(s). 4. 5. 6. 7. Geometry Chapter 7: Right Triangles and Trigonometry 8. 10. 12. 9. 11. 13. Find the area of the triangle.