Geometry

Chapter 7 Review

Algebra Solve each proportion. Show all your work.

1. 2.

3. The ratio of the width to the height of a window is 2 : 7. The width of the window is 3 ft.

Write and solve a proportion to find the height.

4. The angles of a triangle are in the extended ratio of 3 : 5 : 10. Find the measure of each angle.

5. In the proportion a = c

b d b d

Are the triangles similar? If yes, write a similarity statement and explain how you know

they are similar – use a shortcut if you’d like. If not, explainwhy not.

Determine whether the polygons are similar. If so, write a similarity statement
and give the scale factor. If not, explain. Please be careful ♥

8. / 9.

The polygons are similar. Find the value of each variableand the scale factor.

10. 11.

Find the geometric mean of each pair of numbers.

12. 8and1213. 20and6

14. Error Analysis A classmate writes an incorrect proportion to find x. Explain AND correct the error.

15. In∆DEF,theanglebisectorofDintersect at EF at M. EM is 5 inches and MF is 12 inches.

If DE is 17 inches, find the measure of DF.

Algebra Find the value of x.

16 17. 18.

19. Themapattherightshowsthewalkingpathsatalocal park. The garden walkway is parallel to the walkway between the monument and the pond. How long is the path from the pond to the playground?

20.TriangleQRShaslineXYparalleltosideRS.Thelength of QY is 12 in. The length of QX is 8 in.

a.Drawapicturetorepresenttheproblem.

b.IfthelengthofXRis5in.,whatisthelengthofQS?

28.

Word Bank
ratio / proportion / scale factor / similar polygons / indirect measurement / cross products property
geometric mean / side splitter theorem / sponge bob squarepants / extended proportion / extended ratio / scale drawing

24. ______Compares three or more items.

25. ______Is the ratio of corresponding linear measurements of two similar figures.

26. ______Is a comparison of two things, sometimes written as a fraction.

27. ______A drawing where all lengths are proportional to their corresponding actual lengths.

28. ______In a proportion, the means are the same.

29. ______Polygons whose corresponding angles are congruent and the lengths of the corresponding sides are proportional.

30. ______If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

31. ______Two ratios that are equal to each other.

32. ______In an equation, when you multiply the extremes and means to create an equation without a denominator.

33. ______A way to find lengths that are hard to measure directly.

34. ______Three or more ratios are equal.

35. ______He lives in a pineapple under the sea.