2.2 Review Worksheet (continued)

16. Given : ∠ BAC is a right angle. ∠ 2 ≅ ∠ 3 Prove : ∠ 1 and ∠ 3 are complementary. Proof:

B

1

3

2

A

C

Statements

Reasons

1. ∠ BAC is a right angle. 2. m ∠ BAC = 90º 3. b. ? 4. m ∠ 1 + m ∠ 2 = 90º 5. ∠ 2 ≅ ∠ 3 6. c. ? 7. m ∠ 1 + m ∠ 3 = 90º 8. e. ?

1. Given 2. a. ? 3. ∠ Add. Post. 4. Subst. Steps 2, 3 5. Given 6. Def. of ≅ ∠ s 7. d. ? Steps 4, 6 8. Def. of comp. ∠ s

Use the given plan to write a two-column proof. 17. Given : BE ≅ CE , DE ≅ AE Prove : A̅B̅ ≅ CD

D

Plan : Use the definition of congruent segments to write the given information in terms of lengths. Then use the Segment Addition Postulate to show that AB = CD and thus A̅B̅ ≅ CD .

E

A

B

C

18. Given : ∠ 1 and ∠ 3 are complementary, and ∠ 2 and ∠ 4 are complementary. ∠ 3 ≅ ∠ 4 Prove : ∠ 1 ≅ 2 Plan : Since ∠ l and ∠ 3 are complementary and ∠ 2 and ∠ 4

4

1

3

2

are complementary, both pairs of angle measures add to 90º. Use substitution to show that the sums of both pairs are equal. Since ∠ 3 ≅ ∠ 4, their measures are equal. Use the Subtraction Property of Equality and the definition of congruent angles to conclude that ∠ 1 ≅ ∠ 2.

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