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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