Chapter 8 Answers (continued)

Chapter 8 Answers (continued)
Enrichment 8-1
1. 10 lb 2. $250; costs have not changed during the
past year. 3. $240,000 4. $168,750 5. $6785
6. $106 7. 360 yd 8. 40 9. 42 10. 63
Activity 2: Analyzing
Stage 1: 12; 4
1 1
Stage 2: 9 ; 5 3
1 1
Stage 3: 192; 27; 79
Enrichment 8-2
1.–4. Check students’ work.
Enrichment 8-3
1. Statements Reasons
1. ABCD is a trapezoid 1. Given
2. AD 6 BC
2. Def. of a trapezoid
3. AED CEB 3. Vertical angles are .
4. EBC EDA 4. Alt. int. angles are .
5. AED CEB 5. AA Similarity Post.
2. Statements Reasons
1. T, U, and V are mdpts 1. Given
"5
3
2
2. TU 6 RV, UV 6 TR, 2. Triangle Midsegment
and TV 6 US
Theorem
3. TUVR and TUSV are 3. Def. of parallelogram
parallelograms.
4. TUV R 4. Opposite s of a
parallelogram are .
5. UTV S 5. Opposite s of a
parallelogram are .
6. QRS VUT 6. AA Similarity Post.
3. Using the distance formula, AB = "180 or 6 "5,
BC = "45 or 3 "5, CA = 15, ST = 10, TB = "80 or
4 "5,andBS = "20 or 2 . If the two triangles are
CA 15 3 AB 6"5 3 BC 3"5
ST = 10 = 2 = TB = = = = =
4"5
2 BS 2"5
.
similar, then corresponding sides are proportional. Therefore,
CA AB BC
Because ST = TB = BS , ABC TBS by the
SSS Similarity Postulate.
Enrichment 8-4
1. The triangles have two congruent angles; AA Similarity
AB 1 BD AB
(DE 2 BC)AB
Postulate. 2. DE = BC
3. BD = BC
4. 800 yd 5. 4500 ft 6. 43 ft 7. 9 m
Enrichment 8-5
1. 18 2. 1 3. 19 4. 3 5. 8 6. 7 7. 22
8. 9 9. 13 10. 4 11. 5 12. 6 13. 12
14. 17 15. 2 16. 10 17. 21 18. 15 19. 20
20. 16 ARCHIMEDES OF SYRACUSE
Enrichment 8-6
1. 1 : 4 2. 2 : 1 3. 4 : 3 4. 1 : 16
Chapter Project
Activity 1: Doing
Check students’ work.
Activity 3: Doing
Check students’ work.
Activity 4: Thinking
The entire snowflake at each stage will be inside the regular
hexagon. The area of the hexagon is 2 square units, so the area
of the snowflake is always less than 2 square units.
Activity 5: Modeling
Check students’ work.
✔ Checkpoint Quiz 1
6
1.
12
2. 1 : 48 3. 11 4. 6 5. O 6. MO
8 3
7. 3.6 ft 8. no; 20 2 7 9. 780 mi
✔ Checkpoint Quiz 2
1. yes; AA similarity postulate 2. yes; SAS similarity
postulate 3. 5 4. 13.7 5. x = 4.5, y = 7.5
1
6. 8 3
7. 2.5
Chapter 8 Test, Form A
24
2
1. 28 2.
19
3. 45 4.
3
5. ABC XYZ
by the AA Postulate 6. not similar 7. KPM
RPQ by the SAS Theorem 8. 30 ft 9. 9
3
10. 6"5
11. B 12. 12 13. 2
14. 6
18
15. 7 16. Check students’ work. 17. If two parallel
lines are cut by a transversal, alternate interior angles are congruent.
Therefore, ABC EDC by the AA Postulate.
18. 64 : 9 19. 9 : 1 20. x = 9; y = 6 "3;z = 3"3
10 8
60
21. x = 3 ; y = 3
22. C 23.
13
Chapter 8 Test, Form B
9 3
1. 6 2. 12 3. 2
4.
2
5. ABC EDC
by the AA Postulate 6. not similar 7. ABC
RST by the SAS Theorem 8. 24 ft 9. 12
21 45
10. 5"2
11. C 12. 4 13. 4
14.
11
15. 20 16. Check students’ work. 17. Sample: Each
of the two smaller triangles contains a right angle because
the altitude is perpendicular to AC. Also, each of the smaller
triangles shares an angle with ABC. Therefore, each of the
smaller triangles is similar to ABC by the AA Postulate
and, by transitivity, they are similar to each other.
20 15
18. 9 : 4 19. 9 : 1 20. x = 7 ; y = 7 21. x = 30;
y = 8 "15;z = 2"15
22. D 23. 168
25
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Answers Geometry Chapter 8