2.2 Review Worksheet (continued)

2.2.3 Flowchart and Paragraph Proofs 19. Use the given flowchart proof to write a two-column proof. Given : B is the midpoint of AC . AD = EC Prove : DB = BE Flowchart proof:

A D B E C

AD + DB = AB, BE + EC = BC

AD = EC

B is mdpt. of AC .

Given

Seg. Add. Post

Given

AB = BC

AD + DB = BE + EC

DB = BE

AB ≅ BC

Def. of ≅ segs.

Def. of mdpt.

Subst.

Subtr. Prop. of =

20. Use the given two-column proof to write a flowchart proof. Given: ∠ 3 is a right angle. Prove: ∠ 4 is a right angle. Two-column proof:

3

4

Statements

Reasons

1. ∠ 3 is a right angle. 2. m ∠ 3 = 90º 3. ∠ 3 and ∠ 4 are supplementary.

1. Given 2. Def. of rt. ∠ 3. Lin. Pair Thm. 4. Def. of supp. ∠ s 5. Subst. Steps 2, 4 6. Subtr. Prop. of = 7. Def. of rt. ∠

4. m ∠ 3 + m ∠ 4 = 180º 5. 90º + m ∠ 4 = 180º 6. m ∠ 4 = 90º 7. ∠ 4 is a right angle.

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