Geometry

Name: ______________________ Date: _________ Block: ____

Chapter 7 Review Sections 7.1 – 7.3 & 7.5

Things to Know…

Solve the following proportions:

1. 2. 3. 4.

5. Given that 2a = 8b, find the ratio of a to b in simplest form.

Geometry

6. Given that 6x = 27y, find the ratio y : x in simplest form.

7. Given that 5y = 25x, find the ratio of x to y in simplest form.

8. Identify the pairs of congruent angles and corresponding sides.

9. Identify the pairs of congruent angles and corresponding sides.

10. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

11. Explain why the triangles are similar and write a similarity statement.

Geometry

12. Verify that the given triangles are similar.

13. A student wanted to find the height of a statue of a pineapple in Nambour, Australia. She measured the pineapple’s shadow and her own shadow. The student’s height is 5 ft 4 in. What is the height of the pineapple?

14. To find the height of a dinosaur in a museum, Amir placed a mirror on the ground 40 ft from its base. Then he stepped back 4 ft so that he could see the top of the dinosaur in the mirror. Amir’s eyes were approximately 5 ft 6 in. above the ground. What is the height of the dinosaur?

Geometry

15. Given: rectangle MNPQ ∼ rectangle RSTU Find the perimeter of rectangle RSTU. Find the area of rectangle RSTU.

16. Given that rectangle ABCD ∼ EFGH. The area of rectangle ABCD is 135 inches squared. The area of rectangle EFGH is 240 inches squared. If the width of rectangle ABCD is 9 in., what is the length and width of rectangle EFGH?

17. Solve the proportion.

18. Write a ratio expressing the slope of each line m , n and p.

Geometry

19. If 84 is divided into three parts in the ratio 3 : 5 : 6, what is the sum of the smallest and the largest part?

20. The ratio of the measures of a pair of sides of a rectangle is 7 : 12. If the perimeter of the rectangle is 95, what is the length of each side?

21. Solve each proportion.

22. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

rectangles JKLM and PQRS

Geometry

23. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

△TUV and △WXY

24. Complete a proof:

Given: JL = Prove: △JKL ∼ △JMN

25. Complete a proof:

26. Use the dimensions in the diagram to find the height h of the tower. A student who is 5 ft 5 in. tall measured his shadow and a tower’s shadow to find the height of the tower.

Geometry

27. To find the height of a flagpole, Casey measured her own shadow and the flagpole’s shadow. Given that Casey’s height is 5 ft 4 in., what is the height x of the flagpole?

28. Jonathan is 3 ft from a lamppost that is 12 ft high. The lamppost and its shadow form the legs of a right triangle. Jonathan is 6 ft tall and is standing parallel to the lamppost. How long is Jonathan’s shadow?

Define the following vocabulary items:29. cross products

30. extremes

31. indirect measurement

32. means

33. proportion ratio

34. scale

35. scale drawing

Geometry

36. scale factor

37. similar

38.similar polygons

39. similarity ratio

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