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You may use your notes to help you complete these two column proofs. Remember you will use Theorems, Postulates, and Definitions to justify (give reason) to the statements that you are making. Make sure to check your work when you are done. Complete the proof below by dragging the correct reason to each statement being made. 1. ∡3 and ∡4 are complements.
2. m∡3 + m∡4 = 90∘
3. ∡1 ≅ ∡4
4. m∡1 = m∡4
5. m∡3 + m∡1 = 90∘
6. ∡3 and ∡1 are complements. statements Definition of complementary angles. Definition of Complementary angles ? Definition of congruent angles ? Vertical Angle Theorem ? ◄ ◄ reasons Substitution ? Given 1 2 ▲ 5 3 4 ∡2 and ∡3 are supplementary Given: line r // line s prove: ∡1 + ∡2 = 180 ∡1 + ∡2 = 180 ? ∡2 + ∡3 = 180 ? m∡1 = m∡3 ? ∡1 ≅ ∡3 r // s statements Corresponding Angles postulate ? definition of supplementary definition of congruent angles Linear Pair Theorem ? reasons Substitution ? Given ? Complete the proof below by dragging the correct reason to each statement being made. 1. m∡1 + m∡2 = 180∘ 2. m∡2 + m∡3 = 180∘
3. m∡1 + m∡2 = m∡2 + m∡3
4. m∡1 = m∡3
5. ∡1 ≅ ∡3
4. 5. 1. 3. 2. Substitution Property of = ? Subtraction Property of = ? Definition of Congruent angles ? Linear Pair Theorem Linear Pair Theorem ? 1 4 2 3 Complete the proof below by dragging the correct reason to each statement being made. 5. ∡1 = ∡3 + ∡4 4. ∡1 + ∡2 = ∡2 +∡3 + ∡4 3. ∡1 + ∡2 = 180 2. ∡1 and ∡2 are supplementary 1. ∡2 +∡3 + ∡4 = 180o statements not used: Angle Addition Postulate ? 1. 3. 2. 4. 5. Def. of Supplementary ∡'s ? Linear Pair theorem ? Substitution ? Subtraction Property of = ? reasons Given ? |