Proof: Parallel Lines Cut by a Transversal (Geometry)
Free printable Geometry geometry worksheet: complete a two-column proof that alternate interior angles are congruent, using the Corresponding Angles Postulate and the Vertical Angles Theorem.
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Geometry Proof: Parallel Lines Cut by a Transversal
Two parallel lines are cut by a transversal. Complete each two-column proof that a pair of alternate interior angles is congruent, using the Corresponding Angles Postulate and the Vertical Angles Theorem.
- 1.Lines l and m are cut by transversal t, with l ∥ m. Using the standard numbering (angles 1-4 where t crosses l, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where t crosses m, in the same layout), prove ∠3 ≅ ∠6 (a pair of alternate interior angles). Complete the missing reason in step 4 of the two-column proof.
Statement Reason 1.l ∥ m, and t is a transversal of l and m. Given 2.∠3 ≅ ∠7. Corresponding Angles Postulate 3.∠7 ≅ ∠6. Vertical Angles Theorem 4.∠3 ≅ ∠6. - 2.Lines j and k are cut by transversal v, with j ∥ k. Using the standard numbering (angles 1-4 where v crosses j, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where v crosses k, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing reason in step 4 of the two-column proof.
Statement Reason 1.j ∥ k, and v is a transversal of j and k. Given 2.∠4 ≅ ∠8. Corresponding Angles Postulate 3.∠8 ≅ ∠5. Vertical Angles Theorem 4.∠4 ≅ ∠5. - 3.Lines l and m are cut by transversal t, with l ∥ m. Using the standard numbering (angles 1-4 where t crosses l, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where t crosses m, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing reason in step 1 of the two-column proof.
Statement Reason 1.l ∥ m, and t is a transversal of l and m. 2.∠4 ≅ ∠8. Corresponding Angles Postulate 3.∠8 ≅ ∠5. Vertical Angles Theorem 4.∠4 ≅ ∠5. Transitive Property of Congruence - 4.Lines j and k are cut by transversal v, with j ∥ k. Using the standard numbering (angles 1-4 where v crosses j, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where v crosses k, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing statement in step 3 of the two-column proof.
Statement Reason 1.j ∥ k, and v is a transversal of j and k. Given 2.∠4 ≅ ∠8. Corresponding Angles Postulate 3. Vertical Angles Theorem 4.∠4 ≅ ∠5. Transitive Property of Congruence - 5.Lines l and m are cut by transversal t, with l ∥ m. Using the standard numbering (angles 1-4 where t crosses l, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where t crosses m, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing statement in step 1 of the two-column proof.
Statement Reason 1. Given 2.∠4 ≅ ∠8. Corresponding Angles Postulate 3.∠8 ≅ ∠5. Vertical Angles Theorem 4.∠4 ≅ ∠5. Transitive Property of Congruence - 6.Lines l and m are cut by transversal t, with l ∥ m. Using the standard numbering (angles 1-4 where t crosses l, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where t crosses m, in the same layout), prove ∠3 ≅ ∠6 (a pair of alternate interior angles). Complete the missing statement in step 1 of the two-column proof.
Statement Reason 1. Given 2.∠3 ≅ ∠7. Corresponding Angles Postulate 3.∠7 ≅ ∠6. Vertical Angles Theorem 4.∠3 ≅ ∠6. Transitive Property of Congruence - 7.Lines p and q are cut by transversal n, with p ∥ q. Using the standard numbering (angles 1-4 where n crosses p, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where n crosses q, in the same layout), prove ∠3 ≅ ∠6 (a pair of alternate interior angles). Complete the missing reason in step 3 of the two-column proof.
Statement Reason 1.p ∥ q, and n is a transversal of p and q. Given 2.∠3 ≅ ∠7. Corresponding Angles Postulate 3.∠7 ≅ ∠6. 4.∠3 ≅ ∠6. Transitive Property of Congruence - 8.Lines j and k are cut by transversal v, with j ∥ k. Using the standard numbering (angles 1-4 where v crosses j, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where v crosses k, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing reason in step 2 of the two-column proof.
Statement Reason 1.j ∥ k, and v is a transversal of j and k. Given 2.∠4 ≅ ∠8. 3.∠8 ≅ ∠5. Vertical Angles Theorem 4.∠4 ≅ ∠5. Transitive Property of Congruence - 9.Lines l and m are cut by transversal t, with l ∥ m. Using the standard numbering (angles 1-4 where t crosses l, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where t crosses m, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing reason in step 3 of the two-column proof.
Statement Reason 1.l ∥ m, and t is a transversal of l and m. Given 2.∠4 ≅ ∠8. Corresponding Angles Postulate 3.∠8 ≅ ∠5. 4.∠4 ≅ ∠5. Transitive Property of Congruence - 10.Lines p and q are cut by transversal n, with p ∥ q. Using the standard numbering (angles 1-4 where n crosses p, top-left/top-right/bottom-left/bottom-right in order; angles 5-8 where n crosses q, in the same layout), prove ∠4 ≅ ∠5 (a pair of alternate interior angles). Complete the missing statement in step 1 of the two-column proof.
Statement Reason 1. Given 2.∠4 ≅ ∠8. Corresponding Angles Postulate 3.∠8 ≅ ∠5. Vertical Angles Theorem 4.∠4 ≅ ∠5. Transitive Property of Congruence
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