2.2.3 Flowchart and Paragraph Proofs − Worksheet (continued)

Example 2: 3. Use the given paragraph proof to write a two-column proof.

4

Given: ∠ 2 ≅ ∠ 4 Prove: ∠ 1 ≅ ∠ 3 Paragraph proof:

3

2

1

By the Vertical Angles Theorem, ∠ 1 ≅ ∠ 2, and ∠ 3 ≅ ∠ 4. It is given that ∠ 2 ≅ ∠ 4. By the Transitive Property of Congruence, ∠ 1 ≅ ∠ 4, and thus ∠ 1 ≅ ∠ 3.

Example 3: 4. Use the given two-column proof to write a paragraph proof. Given: ∠ BD ABC bisects . Prove: ∠ BG FBH bisects . Two-column proof:

A

F

B

1

3 4

2

D

G

C

H

Statements

Reasons

1. 2. ∠ 1 ≅ ∠ 2 3. ∠ 1 ≅ ∠ 4, ∠ 2 ≅ ∠ 3 ∠ ABC bisects . BD

1. Given 2. Def. of ∠ bisector 3. Vert. ∠ s Thm.

4. Trans. Prop. of ≅ Steps 2, 3 5. Trans. Prop. of ≅ Steps 3, 4 6. Def. of ∠ bisector

4. ∠ 4 ≅ ∠ 2 5. ∠ 4 ≅ ∠ 3 6. BG

∠ FBH bisects .

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