2.2.3 Flowchart and Paragraph Proofs − Practice (continued)

5. Write a paragraph proof to prove that ∠ 2 and ∠ 3 are complementary given that ∠ 1 and ∠ 2 are complementary, and m ∠ 1 = m ∠ 3.

6. Write a justification for each step, given that NS intersects MR , m ∠ MPN = 35° and m ∠ RPQ = 55°.

It is given that NS intersects MR . By the ________, ∠ MPN and ∠ SPR are vertical ∠ s. By the ________, ∠ MPN ≅ ∠ SPR . By the ________, m ∠ MPN = m ∠ SPR . It is given that m ∠ MPN = 35°. So, m ∠ SPR = 35° by the ________. By the ________, m ∠ SPQ = m ∠ SPR + m ∠ RPQ . It is given that m ∠ RPQ = 55°. So, m ∠ SPQ = 35° + 55° by the ________. Simplify to get m ∠ SPQ = 90°. Thus, ∠ SPQ is a right ∠ by ________.

121

Made with FlippingBook - Online magazine maker