2.2 Review Worksheet (continued)
2.2.2 Geometric Proof 14. Write a justification for each step, given that BX
bisects ∠ ABC and m ∠ XBC = 45º.
1. BX
bisects ∠ ABC.
2. ∠ ABX ≅ ∠ XBC 3. m ∠ ABX = m ∠ XBC
A
4. m ∠ XBC = 45º 5.m ∠ ABX = 45º 6.m ∠ ABX + m ∠ XBC = m ∠ ABC 7. 45º + 45º = m ∠ ABC 8. 90º = m ∠ ABC 9. ∠ ABC is a right angle.
X
B
C
Fill in the blanks to complete each two-column proof. 15. Given : ∠ 1 and ∠ 2 are supplementary, and ∠ 3 and ∠ 4 are supplementary. ∠ 2 ≅ ∠ 3 Prove : ∠ 1 ≅ ∠ 4 Proof:
1
2
3
4
Statements
Reasons
Statements
Reasons
1. ∠ 1 and ∠ 2 are supplementary. ∠ 3 and ∠ 4 are supplementary. 2. a. _______ 3. m ∠ 1 + m ∠ 2 – m ∠ 3 + m ∠ 4 4. ∠ 2 ≅ ∠ 3 5. m ∠ 2 – m ∠ 3 6. c . _______ 7. ∠ 1 ≅ ∠ 4 ? ?
1. Given 1. Given 2. Def. of supp. ∠ s 2. Def. of supp. ∠ 3 3. b . _______ 4. Given 5. Def. of ≅ ∠ 3 6. Subtr. Prop. of = Steps 3, 5 7. d . ___?____ ? 3. b. ? 4. Given 5. Def. of ≅ ∠ s 6. Subtr. Prop. of = Steps 3, 5 7. d. ?
1. ∠ 1 and ∠ 2 are supplementary. ∠ 3 and ∠ 4 are supplementary. 2. a. ? 3. m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 4 4. ∠ 2 ≅ ∠ 3 5. m ∠ 2 = m ∠ 3 6. c. ? 7. ∠ 1 ≅ ∠ 4
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