GEOMETRY - HW#31 Name____________________________ Sections 3.1 – 3.4 Review Date__________________Period_____ Complete the following proofs.

1. a. 9 = 4𝑥 − 3(𝑥 − 2) a. Given

b. 9 = 4𝑥 − 3𝑥 + 6 b. Distributive or Multiplication Property of Equality

c. 9 = 𝑥 + 6 c. Subtraction of Like Terms / Simplify

d. 3 = 𝑥 d. Subtraction Property of Equality

e. 𝑥 = 3 e. Symmetric Property of Equality

2. a. 𝐴𝐵 = 𝐶𝐷 a. Given

b. 𝐵𝐶 = 𝐵𝐶 b. Reflexive Property of Equality

c. 𝐴𝐵 + 𝐵𝐶 = 𝐶𝐷 + 𝐵𝐶 c. Addition Property of Equality

d. 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶 d. Segment Addition Postulate

e. 𝐶𝐷 + 𝐵𝐶 = 𝐵𝐷 e. Segment Addition Postulate

f. 𝐴𝐶 = 𝐵𝐷 f. Substitution Property of Equality

3. a. 𝐴𝐷 a. Given

b. 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶 b. Segment Addition Postulate

c. 𝐴𝐶 + 𝐶𝐷 = 𝐴𝐷 c. Segment Addition Postulate

d. 𝐴𝐵 + 𝐵𝐶 + 𝐶𝐷 = 𝐴𝐷 d. Substitution Property of Equality

4. a. 𝑃𝑜𝑖𝑛𝑡𝑠 𝑃, 𝑄, 𝑅, 𝑎𝑛𝑑 𝑆 𝑎𝑟𝑒 𝑐𝑜𝑙𝑙𝑖𝑛𝑒𝑎𝑟 a. Given

b. 𝑃𝑄 + 𝑄𝑆 = 𝑃𝑆 b. Segment Addition Postulate

c. 𝑃𝑄 = 𝑃𝑆 − 𝑄𝑆 c. Subtraction Property of Equality

d. 𝑃𝑆 − 𝑄𝑆 = 𝑃𝑄 d. Symmetric Property of Equality

e. 𝑃𝑆 − 𝑄𝑆 = 𝑃𝑄 e. Reflexive Property of Equality

5. a. 𝐴𝐶 ≅ 𝐷𝐹 a. Given

b. 𝐴𝐵 ≅ 𝐷𝐸 b. Given

c. 𝐴𝐶 = 𝐷𝐹 c. Definition of Congruent Segments

d. 𝐴𝐵 = 𝐷𝐸 d. Definition of Congruent Segments

e. 𝐴𝐶 = 𝐴𝐵 + 𝐵𝐶 e. Segment Addition Postulate

f. 𝐷𝐹 = 𝐷𝐸 + 𝐸𝐹 f. Segment Addition Postulate

g. 𝐴𝐵 + 𝐵𝐶 = 𝐷𝐸 + 𝐸𝐹 g. Substitution or Addition Property of Equality

h. 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐵 + 𝐸𝐹 h. Substitution Property of Equality

i. 𝐵𝐶 = 𝐸𝐹 i. Subtraction Property of Equality

j. 𝐵𝐶 ≅ 𝐸𝐹 j. Definition of Congruent Segments

Complete the following proofs. 6. a. 𝑚∠1 = 24° a. Given

b. 24° = 𝑚∠3 b. Given

c. 𝑚∠1 = 𝑚∠3 c. Transitive or Substitution Property of Equality

d. ∠1 ≅ ∠3 d. Definition of Congruent Angles

e. 𝑚∠1 + 𝑚∠2 = 90° e. Definition of Complementary Angles

f. 𝑚∠3 + 𝑚∠4 = 90° f. Definition of Complementary Angles

g. ∠2 ≅ ∠4 g. Congruent Complements Theorem

7. a. 𝐴𝐵 ≅ 𝐵𝐶 a. Given

b. 𝐴𝐵 = 𝐵𝐶 b. Definition of Congruent Segments

c. 𝐴𝐶 = 𝐴𝐵 + 𝐵𝐶 c. Segment Addition Postulate

d. 𝐴𝐶 = 𝐵𝐶 + 𝐵𝐶 d. Substitution Property of Equality

e. 𝐴𝐶 = 2 ∙ 𝐵𝐶 e. Addition Property of Equality

f. 1

2𝐴𝐶 = 𝐵𝐶 f. Division Property of Equality

Use the property to complete the statement.

8. Reflexive property of equality: 𝑋𝑌𝑍 = 𝑿𝒀𝒁.

9. Transitive property of equality: 𝐼𝑓 𝑈𝑉 = 𝑊𝑋, 𝑎𝑛𝑑 𝑾𝑿 = 𝑌𝑍, 𝑡ℎ𝑒𝑛 𝑼𝑽 = 𝒀𝒁.

10. Subtraction property of equality: 𝐼𝑓 𝑥 = 6, 𝑡ℎ𝑒𝑛 𝑥 − 4 = 2.

11. Symmetric property of equality: 𝐼𝑓 𝐷𝐸 = 𝐹𝐺, 𝑡ℎ𝑒𝑛 𝑭𝑮 = 𝑫𝑬.

12. Multiplication property of equality: 𝐼𝑓 𝑚∠𝐴 = 60°, 𝑡ℎ𝑒𝑛 𝟏

𝟔 (𝑚∠𝐴) = 10°

13. Addition property of equality: 𝐼𝑓 ∠𝐴𝐵𝐶 = 75°, 𝑡ℎ𝑒𝑛 18° + 𝑚∠𝐴𝐵𝐶 = 𝟗𝟑°.

14. Substitution property of equality: 𝐼𝑓 ∠𝐴𝐵𝐶 = 75°, 𝑡ℎ𝑒𝑛 3(𝑚∠𝐴𝐵𝐶) = 𝟐𝟐𝟓°.

Complete the statement given that 𝑚∠𝐵𝐻𝐷 = 𝑚∠𝐶𝐻𝐸 = 𝑚∠𝐸𝐻𝐹 = 90𝑜. 15. 𝐼𝑓 𝑚∠3 = 28𝑜, 𝑡ℎ𝑒𝑛 𝑚∠6 = 𝟐𝟖°. 16. 𝐼𝑓 𝑚∠𝐵𝐻𝐸 = 121𝑜, 𝑡ℎ𝑒𝑛 𝑚∠1 = 𝟑𝟏°. 17. 𝐼𝑓 𝑚∠1 = 34𝑜, 𝑡ℎ𝑒𝑛 𝑚∠6 = 𝟑𝟒°. 18. 𝐼𝑓 𝑚∠𝐸𝐻𝐺 = 158𝑜, 𝑡ℎ𝑒𝑛 𝑚∠7 = 𝟔𝟖°. 19. 𝐼𝑓 𝑚∠7 = 31𝑜, 𝑡ℎ𝑒𝑛 𝑚∠3 = 𝟓𝟗°. 20. 𝐼𝑓 𝑚∠𝐸𝐻𝐵 = 119𝑜, 𝑡ℎ𝑒𝑛 𝑚∠2 = 𝟔𝟏°.

21. Find the 𝑚∠1 and 𝑚∠2. 22. Find the 𝑚∠1 and 𝑚∠2.

𝟕𝒙 + 𝟐 + 𝟑𝒙 + 𝟖 = 𝟏𝟖𝟎° 𝟒𝒙 − 𝟏𝟕 = 𝟐𝒙 + 𝟗

𝒙 = 𝟏𝟕 𝒙 = 𝟏𝟑 𝒎∠𝟏 = 𝟓𝟗°, 𝒎∠𝟐 = 𝟏𝟐𝟏° 𝒎∠𝟏 𝒂𝒏𝒅 𝒎∠𝟐 = 𝟏𝟒𝟓°