Presentation on theme: "Flowchart and Paragraph Proofs"— Presentation transcript:
1Flowchart and Paragraph Proofs 2-7Flowchart and Paragraph ProofsWarm UpLesson PresentationLesson QuizHolt McDougal GeometryHolt Geometry
2Warm Up Complete each sentence. 1. If the measures of two angles are ? , then the angles are congruent.2. If two angles form a ? , then they are supplementary.3. If two angles are complementary to the same angle, then the two angles are ? .equallinear paircongruent
3Objectives Write flowchart and paragraph proofs. Prove geometric theorems by using deductive reasoning.
15A 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.
17Example 3: Reading a Paragraph Proof 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°.
18Statements Reasons Example 3 Continued Two-column proof: 1. m1 + m2 = m41. Given2. 3 and 4 are supp.2. Linear Pair Theorem3. m3 + m4 = 180°3. Def. of supp. s4. m3 + m1 + m2 = 180°4. Substitution
19Check It Out! Example 3Use 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.
20Check It Out! Example 3 Continued StatementsReasons1. WXY is a right angle.1. Given2. 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
21Example 4: Writing a Paragraph Proof 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.
23Check It Out! Example 4Use the given two-column proof to write a paragraph proof.Given: 1 4Prove: 2 3Two-column proof:
24Check It Out! Example 4 Continued Paragraph proof:It is given that 1 4. By the Vertical Angles Theorem, 1 2 and 3 4. By the Transitive Property of Congruence, 2 4. Also by the Transitive Property of Congruence, 2 3.
25Lesson QuizUse the two-column proof at right to write the following.1. a flowchart proof2. a paragraph proof