Activity 4: Complete the proof of the Alternate Interior Angles Theorem. Given: $m \parallel n$ Prove: $\angle3 \cong \angle6$ 1. 2. $\angle3 \cong \angle2$ 3. 4. Statement Reasons 1. 2. 3. Corresponding Angles Postulate 4. Transitive Property of Angle Congruence
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Statement 3: ∠0J is a corresponding angle to ∠26 Reason: By definition of corresponding angles. Statement 4: ∠0J ≅ ∠26 Reason: By Statement 2 and Statement 3, ∠0J and ∠26 are corresponding angles and therefore congruent. Statement 5: Transitive Show more…
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Given: a // b and ∠1 ≅ ∠2 Reason Word Bank: Prove: ∠3 ≅ ∠4 Alternate Interior Angle Theorem Alternate Exterior Angle Theorem Corresponding Angle Postulate Same-side Interior Angle Theorem Converse of Alternate Interior Angle Thm. Converse of Alternate Exterior Angle Thm. Converse of Corresponding Angle Post. Converse of Same-side Interior Angle Thm. Transitive Property Substitution Property Statements Reasons 1. a // b 1. Given 2. 2. Corresponding Angles Post. (step 1) 3. ∠1 ≅ ∠2 3. Given 4. 4. Transitive Property (step 2 & 3) 5. ∠2 ≅ ∠3 5. (step 1) 6. 6. (step 4 & 5)
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