2.2.2 Geometric Proof − Worksheet

Example 1: 1. Write a justification for each step, given that m ∠ A = 60° and m ∠ B = 2m ∠ A. 1.m ∠ A = 60°, m ∠ B = 2m ∠ A 2.m ∠ B = 2(60°) 3.m ∠ B = 120° 4.m ∠ A + m ∠ B = 60° + 120° 5.m ∠ A + m ∠ B = 180° 6. ∠ A and ∠ B are supplementary.

A B

Example 2: 2. Fill in the blanks to complete the two-column proof. Given: ∠ 2 ≅ ∠ 3 Prove: ∠ 1 and ∠ 3 are supplementary. Proof:

3

1 2

Statements

Reasons

1. ∠ 2 ≅ ∠ 3 2. m ∠ 2 = m ∠ 3 3. b. ?

1. Given 2. a. ? 3. Lin. Pair Thm. 4. Def. of Supp. ∠ s 5. c. ? Steps 2, 4 6. Def. of Supp. ∠ s

4. m ∠ 1 + m ∠ 2 = 180º 5. m ∠ 1 + m ∠ 3 = 180º 6. d. ?

Example 3: 3. Use the given plan to write a two-column proof. Given: X is the midpoint of AY , and Y is the midpoint of XB . Prove: AX ≅ YB Plan: By the definition of midpoint, AX ≅ XY , and XY ≅ YB . Use the Transitive Property to conclude that AX ≅ YB .

A X Y B

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