Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
GEOMETRY - HW#31 Name____________________________ Sections 3.1 โ 3.4 Review Date__________________Period_____ Complete the following proofs.
1. a. 9 = 4๐ฅ โ 3(๐ฅ โ 2) a. Given
b. 9 = 4๐ฅ โ 3๐ฅ + 6 b. Distributive or Multiplication Property of Equality
c. 9 = ๐ฅ + 6 c. Subtraction of Like Terms / Simplify
d. 3 = ๐ฅ d. Subtraction Property of Equality
e. ๐ฅ = 3 e. Symmetric Property of Equality
2. a. ๐ด๐ต = ๐ถ๐ท a. Given
b. ๐ต๐ถ = ๐ต๐ถ b. Reflexive Property of Equality
c. ๐ด๐ต + ๐ต๐ถ = ๐ถ๐ท + ๐ต๐ถ c. Addition Property of Equality
d. ๐ด๐ต + ๐ต๐ถ = ๐ด๐ถ d. Segment Addition Postulate
e. ๐ถ๐ท + ๐ต๐ถ = ๐ต๐ท e. Segment Addition Postulate
f. ๐ด๐ถ = ๐ต๐ท f. Substitution Property of Equality
3. a. ๐ด๐ท a. Given
b. ๐ด๐ต + ๐ต๐ถ = ๐ด๐ถ b. Segment Addition Postulate
c. ๐ด๐ถ + ๐ถ๐ท = ๐ด๐ท c. Segment Addition Postulate
d. ๐ด๐ต + ๐ต๐ถ + ๐ถ๐ท = ๐ด๐ท d. Substitution Property of Equality
4. a. ๐๐๐๐๐ก๐ ๐, ๐, ๐ , ๐๐๐ ๐ ๐๐๐ ๐๐๐๐๐๐๐๐๐ a. Given
b. ๐๐ + ๐๐ = ๐๐ b. Segment Addition Postulate
c. ๐๐ = ๐๐ โ ๐๐ c. Subtraction Property of Equality
d. ๐๐ โ ๐๐ = ๐๐ d. Symmetric Property of Equality
e. ๐๐ โ ๐๐ = ๐๐ e. Reflexive Property of Equality
5. a. ๐ด๐ถ โ ๐ท๐น a. Given
b. ๐ด๐ต โ ๐ท๐ธ b. Given
c. ๐ด๐ถ = ๐ท๐น c. Definition of Congruent Segments
d. ๐ด๐ต = ๐ท๐ธ d. Definition of Congruent Segments
e. ๐ด๐ถ = ๐ด๐ต + ๐ต๐ถ e. Segment Addition Postulate
f. ๐ท๐น = ๐ท๐ธ + ๐ธ๐น f. Segment Addition Postulate
g. ๐ด๐ต + ๐ต๐ถ = ๐ท๐ธ + ๐ธ๐น g. Substitution or Addition Property of Equality
h. ๐ด๐ต + ๐ต๐ถ = ๐ด๐ต + ๐ธ๐น h. Substitution Property of Equality
i. ๐ต๐ถ = ๐ธ๐น i. Subtraction Property of Equality
j. ๐ต๐ถ โ ๐ธ๐น j. Definition of Congruent Segments
Complete the following proofs. 6. a. ๐โ 1 = 24ยฐ a. Given
b. 24ยฐ = ๐โ 3 b. Given
c. ๐โ 1 = ๐โ 3 c. Transitive or Substitution Property of Equality
d. โ 1 โ โ 3 d. Definition of Congruent Angles
e. ๐โ 1 + ๐โ 2 = 90ยฐ e. Definition of Complementary Angles
f. ๐โ 3 + ๐โ 4 = 90ยฐ f. Definition of Complementary Angles
g. โ 2 โ โ 4 g. Congruent Complements Theorem
7. a. ๐ด๐ต โ ๐ต๐ถ a. Given
b. ๐ด๐ต = ๐ต๐ถ b. Definition of Congruent Segments
c. ๐ด๐ถ = ๐ด๐ต + ๐ต๐ถ c. Segment Addition Postulate
d. ๐ด๐ถ = ๐ต๐ถ + ๐ต๐ถ d. Substitution Property of Equality
e. ๐ด๐ถ = 2 โ ๐ต๐ถ e. Addition Property of Equality
f. 1
2๐ด๐ถ = ๐ต๐ถ f. Division Property of Equality
Use the property to complete the statement.
8. Reflexive property of equality: ๐๐๐ = ๐ฟ๐๐.
9. Transitive property of equality: ๐ผ๐ ๐๐ = ๐๐, ๐๐๐ ๐พ๐ฟ = ๐๐, ๐กโ๐๐ ๐ผ๐ฝ = ๐๐.
10. Subtraction property of equality: ๐ผ๐ ๐ฅ = 6, ๐กโ๐๐ ๐ฅ โ 4 = 2.
11. Symmetric property of equality: ๐ผ๐ ๐ท๐ธ = ๐น๐บ, ๐กโ๐๐ ๐ญ๐ฎ = ๐ซ๐ฌ.
12. Multiplication property of equality: ๐ผ๐ ๐โ ๐ด = 60ยฐ, ๐กโ๐๐ ๐
๐ (๐โ ๐ด) = 10ยฐ
13. Addition property of equality: ๐ผ๐ โ ๐ด๐ต๐ถ = 75ยฐ, ๐กโ๐๐ 18ยฐ + ๐โ ๐ด๐ต๐ถ = ๐๐ยฐ.
14. Substitution property of equality: ๐ผ๐ โ ๐ด๐ต๐ถ = 75ยฐ, ๐กโ๐๐ 3(๐โ ๐ด๐ต๐ถ) = ๐๐๐ยฐ.
Complete the statement given that ๐โ ๐ต๐ป๐ท = ๐โ ๐ถ๐ป๐ธ = ๐โ ๐ธ๐ป๐น = 90๐. 15. ๐ผ๐ ๐โ 3 = 28๐, ๐กโ๐๐ ๐โ 6 = ๐๐ยฐ. 16. ๐ผ๐ ๐โ ๐ต๐ป๐ธ = 121๐, ๐กโ๐๐ ๐โ 1 = ๐๐ยฐ. 17. ๐ผ๐ ๐โ 1 = 34๐, ๐กโ๐๐ ๐โ 6 = ๐๐ยฐ. 18. ๐ผ๐ ๐โ ๐ธ๐ป๐บ = 158๐, ๐กโ๐๐ ๐โ 7 = ๐๐ยฐ. 19. ๐ผ๐ ๐โ 7 = 31๐, ๐กโ๐๐ ๐โ 3 = ๐๐ยฐ. 20. ๐ผ๐ ๐โ ๐ธ๐ป๐ต = 119๐, ๐กโ๐๐ ๐โ 2 = ๐๐ยฐ.
21. Find the ๐โ 1 and ๐โ 2. 22. Find the ๐โ 1 and ๐โ 2.
๐๐ + ๐ + ๐๐ + ๐ = ๐๐๐ยฐ ๐๐ โ ๐๐ = ๐๐ + ๐
๐ = ๐๐ ๐ = ๐๐ ๐โ ๐ = ๐๐ยฐ, ๐โ ๐ = ๐๐๐ยฐ ๐โ ๐ ๐๐๐ ๐โ ๐ = ๐๐๐ยฐ