15 Student guided practice Do problems 7 and 8 from your book page 123
16 Paragraph proofs What are paragraph proofs? A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step.
18 Example Use the given paragraph proof to write a two- column proof. Given: m1 + m2 = m4Prove: m3 + m1 + m2 = 180°Paragraph Proof: It is given thatm1 + m2 = m4. 3 and 4 aresupplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°.
20 Example#2 Use the given paragraph proof to write a two- column proof. Given: WXY is a right angle. 1 3Prove: 1 and 2 are complementary.Paragraph Proof: Since WXY is a right angle, mWXY = 90° by the definition of a right angle. By the Angle Addition Postulate, mWXY = m2 + m3. By substitution, m2 + m3 = 90°. Since 1 3, m1 = m3 by the definition of congruent angles. Using substitution, m2 + m1 = 90°. Thus by the definition of complementary angles, 1 and 2 are complementary.
21 Solution Statements Reasons 1. WXY is a right angle. 1. Given 2. mWXY = 90°2. Def. of right angle3. m2 + m3 = mWXY3. Angle Add. Postulate4. m2 + m3 = 90°4. Subst.5. 1 35. Given6. m1 = m36. Def. of s7. m2 + m1 = 90°7. Subst.8. 1 and 2 are comp.8. Def. of comp. angles
22 Example Use the given two-column proof to write a paragraph proof. Given: 1 and 2 are complementaryProve: 3 and 4 are complementarym3 + m4 = 90°3 and 4 are comp.