Geometry Name _____________________________________ REVIEW: Chapter 7 1. Given the choice between doing an oral and a written report, 18 of the 28 students chose to do an oral report. Find the ratio of written to oral reports. 2. A model of a lighthouse has diameter 8 inches and height 18 inches. If the actual diameter of the lighthouse is 20 feet, find its actual height. 3. The three sides of a triangle are in the ratio 2:4:5. If the perimeter is 77 meters, find the length of the shortest side. 4. Find the polygon that is similar to ABCD. a) b) c) d) 5. If ∆ABC ~ ∆DEF, find m∠C. 6. Quadrilateral JKLM ~ quadrilateral WXYZ, JK = 15, LM = 10, XY = 6, and WX = 9.

a) Find KL. b) What is the scale factor of Quadrilateral JKLM to Quadrilateral WXYZ

7. ∆LMN ~ ∆RST, LN = 21, MN =28, and the scale factor of ∆RST to ∆LMN is 43

. Find ST.

8. Name the theorem or postulate that can be used to prove that these triangles are similar. a) AA Similarity b) SSA Similarity c) SAS Similarity d) SSS Similarity 9. Identify the similar triangles. a) ∆LMN ~ ∆MPQ b) ∆LMN ~ ∆QPM c) ∆LMN ~ ∆QMP d) ∆LMN ~ ∆PQM 10. Using the diagram from number 9 above, find LM. 11. A 6-foot-tall fence post cast a 2 ½-foot shadow. At the same time, a nearby clock tower cast a 35-foot shadow. What is the height of the tower? 12.a) Find CD. b) Find CE. 13. Find FH so that 𝐺𝐻 ∥ 𝐷𝐸. 14. Find the value of x.

15. Determine whether 𝐷𝐸���� ∥ 𝐵𝐶����. Justify your answer with math AND in words. 16. ∆ABC ~ ∆XYZ with altitudes 𝐴𝑃 and 𝑋𝑄. Find AP. 17. Find the value of x. 18. Find the value of y.

19. Find the value of x. 20. △ABC ∼ △PQR, AB = 18, BC = 20, AC = 22, and QR = 25. Find the perimeter of △PQR.

2 3

87

ED

C

A

B