Chapter 7 Test Review This is to review for your upcoming test Be honest with yourself, can you complete all the problems on you own? HELP!! On successnet, you can complete more similar problems in the explore center. Can you draw images that show the 3 theorems about similarity? Ask Questions!!! Put this show in powerpoint mode and try to complete all the questions on your own. The answers are at the end to check when you finish (26 problems)

Chapter Review 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion. 2.

3. Given that 14a = 35b, find the ratio of a to b in simplest form.

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

5. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is. If the length of the model is 10 inches, what is the length of the actual sailboat in feet?

6. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar.

use ∆RST. 7. Write a similarity statement comparing the three triangles. 8. If PS = 6 and PT = 9, find PR.

use ∆RST. 9. If TP = 24 and PR = 6, find RS. 10. Complete the equation (ST) 2 = (TP + PR)(?).

Find the length of each segment. 11.

Find the length of each segment. 12.

13. The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle?

14. Given that 18c = 24d, find the ratio of d to c in simplest form.

15. Verify that the triangles are similar. ∆PQR and ∆STU

16. Verify that ∆TXU ~ ∆VXW.

17. Explain why ∆ABE ~ ∆ACD, and then find CD.

18.Explain why ∆RSV ~ ∆RTU and then find RT.

19. The photo shows a gable roof. AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot.

20. Write a similarity statement comparing the three triangles.

21. Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 4 and 25

22. Find x, y, and z.

23. Find PS and SR.

24. Find AC and DC.

25. A surveyor positions himself so that his line of sight to the top of a cliff and his line of sight to the bottom form a right angle as shown. What is the height of the cliff to the nearest foot?

To estimate the height of a Douglas fir, Jan positions herself so that her lines of sight to the top and bottom of the tree form a 90º angle. Her eyes are about 1.6 m above the ground, and she is standing 7.8 m from the tree. What is the height of the tree to the nearest meter? 26.

Answers

Chapter Review 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion °, 75°, 90° 3

3. Given that 14a = 35b, find the ratio of a to b in simplest form.

4. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. no

5. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is. If the length of the model is 10 inches, what is the length of the actual sailboat in feet? 25 ft

6. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar. Always

use ∆RST. 7. Write a similarity statement comparing the three triangles. 8. If PS = 6 and PT = 9, find PR. ∆RST ~ ∆RPS ~ ∆SPT 4

use ∆RST. 9. If TP = 24 and PR = 6, find RS. 10. Complete the equation (ST) 2 = (TP + PR)(?). TP

Find the length of each segment. 11.

Find the length of each segment. 12. SR = 25, ST = 15

13. The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle? x + y + z = 180° x + 6x + 13x = 180° 20x = 180° x = 9° y = 6x y = 6(9°) y = 54° z = 13x z = 13(9°) z = 117°

14. Given that 18c = 24d, find the ratio of d to c in simplest form. 18c = 24d Divide both sides by 24c. Simplify.

15. Verify that the triangles are similar. ∆PQR and ∆STU Therefore ∆PQR ~ ∆STU by SSS ~.

16. Verify that ∆TXU ~ ∆VXW.  TXU   VXW by the Vertical Angles Theorem. Therefore ∆TXU ~ ∆VXW by SAS ~.

 A   A by Reflexive Property of , and  B   C since they are both right angles. 17. Explain why ∆ABE ~ ∆ACD, and then find CD. Step 1 Prove triangles are similar. Therefore ∆ABE ~ ∆ACD by AA ~.

18.Explain why ∆RSV ~ ∆RTU and then find RT. Step 1 Prove triangles are similar. It is given that  S   T.  R   R by Reflexive Property of . Therefore ∆RSV ~ ∆RTU by AA ~.

19. The photo shows a gable roof. AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot. From p. 473, BF  4.6 ft. BA = BF + FA   23.3 ft Therefore, BA = 23.3 ft.

20. Write a similarity statement comparing the three triangles. Sketch the three right triangles with the angles of the triangles in corresponding positions. By Theorem 8-1-1, ∆LJK ~ ∆JMK ~ ∆LMJ.

21. Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 4 and 25 Let x be the geometric mean. x 2 = (4)(25) = 100Def. of geometric mean x = 10Find the positive square root.

22. Find x, y, and z. 6 2 = (9)(x) 6 is the geometric mean of 9 and x. x = 4 Divide both sides by 9. y 2 = (4)(13) = 52 y is the geometric mean of 4 and 13. Find the positive square root. z 2 = (9)(13) = 117 z is the geometric mean of 9 and 13. Find the positive square root.

23. Find PS and SR. Substitute the given values. Cross Products Property Distributive Property by the ∆  Bisector Theorem. 40(x – 2) = 32(x + 5) 40x – 80 = 32x + 160

24. Find AC and DC. Substitute in given values. Cross Products Theorem So DC = 9 and AC = 16. Simplify. by the ∆  Bisector Theorem. 4y = 4.5y – 9 –0.5y = –9 Divide both sides by –0.5. y = 18

25. The cliff is about , or 148 ft high. Let x be the height of cliff above eye level. (28) 2 = 5.5x 28 is the geometric mean of 5.5 and x. Divide both sides by 5.5. x  142.5

26. Let x be the height of the tree above eye level. x = ≈ 38 (7.8) 2 = 1.6x The tree is about = 39.6, or 40 m tall. 7.8 is the geometric mean of 1.6 and x. Solve for x and round.