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Geometry 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Learning Objective: Students will use 3 different methods to prove geometric relationships (2 column proof, flowchart, and paragraph form) Learning Target 2A I can connect reasoning in algebra and geometry by justifying steps in a logical argument. Geometry 2-6 Proving Geometric Relationships Page 59 Prove the following using “Paragraph form” (write underneath flowchart): Prove the following using two columns Flowchart proof, or flow proof A proof which uses boxes and arrows to show the flow of a logical argument. Paragraph Proof A proof which presents the statements and reasons of a proof as sentences in a paragraph. It uses words to explain the logical flow of the argument. Geometry 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Page 61 Theorem 2.3 Right Angles Congruence Theorem All right angles are congruent. Geometry 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Page 61 Theorem 2.4 Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. If ∠1 and ∠2 are supplementary and ∠3 and ∠2 are supplementary then ∠1 ≅ ∠3. Geometry 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Page 62 Theorem 2.5 Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles), then they are congruent. If ∠4 and ∠5 are complementary and ∠6 and ∠5 are complementary then ∠4 ≅ ∠6. Geometry 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Page 62 Postulate 2.8 Linear Pair Postulate If two angles form a linear pair, then they are supplementary. ∠1 and ∠2 form a linear pair so ∠1 and ∠2 are supplementary and 𝑚∠1 + 𝑚∠2 = 180. Geometry 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Page 62 Theorem 2.6 Vertical Angles Congruence Theorem Vertical angles are congruent. Geometry Page 62 2-6 Proving Geometric POINTS, LINES ANDRelationships PLANES Geometry 2-6 Proving Geometric Relationships Not in book Geometry 2-6 Proving Geometric Relationships Not in book Geometry 2-6 Proving Geometric Relationships Not in book Use the diagram and the given angle measure to find the other three angle measures. 1. 𝑚∠1 = 117°. Geometry 2-6 Proving Geometric Relationships Not in book Use the diagram and the given angle measure to find the other three angle measures. 2. 𝑚∠2 = 59°. Geometry 2-6 Proving Geometric Relationships Not in book Use the diagram and the given angle measure to find the other three angle measures. 3. 𝑚∠4 = 88°. Geometry 2-6 Proving Geometric Relationships Not in book Use the diagram and the given angle measure to find the other three angle measures. 4. Find the value of w Geometry Prove that Vertical Angles are Congruent Use the word bank below to prove the theorem. ∠1 & ∠2 are vertical angles 𝑚∠2 + 𝑚∠3 = 180 Segment Addition Postulate Substitution Angle Addition Postulate Given Subtraction Property Prove the Vertical Angles Theorem Given: ∠1 and ∠2 are vertical Prove: ∠1 ≅ ∠2 Statements a. c. 𝑚∠1 + 𝑚∠3 = 180 e. g. 𝑚∠1 + 𝑚∠3 = 𝑚∠2 + 𝑚∠3 i. 𝑚∠1 = 𝑚∠2 or ∠1 ≅ ∠2 Reasons b. d. f. Angle addition postulate h. j.