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.

Lines l and m are cut by transversal t, with l

\parallel

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

\angle 3

\cong

\angle 6

(a pair of alternate interior angles). Complete the missing reason in step 4 of the two-column proof.

Statement	Reason
1.l $\parallel$ m, and t is a transversal of l and m.	Given
2. $\angle 3$ $\cong$ $\angle 7$ .	Corresponding Angles Postulate
3. $\angle 7$ $\cong$ $\angle 6$ .	Vertical Angles Theorem
4. $\angle 3$ $\cong$ $\angle 6$ .

Lines j and k are cut by transversal v, with j

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing reason in step 4 of the two-column proof.

Statement	Reason
1.j $\parallel$ k, and v is a transversal of j and k.	Given
2. $\angle 4$ $\cong$ $\angle 8$ .	Corresponding Angles Postulate
3. $\angle 8$ $\cong$ $\angle 5$ .	Vertical Angles Theorem
4. $\angle 4$ $\cong$ $\angle 5$ .

Lines l and m are cut by transversal t, with l

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing reason in step 1 of the two-column proof.

Statement	Reason
1.l $\parallel$ m, and t is a transversal of l and m.
2. $\angle 4$ $\cong$ $\angle 8$ .	Corresponding Angles Postulate
3. $\angle 8$ $\cong$ $\angle 5$ .	Vertical Angles Theorem
4. $\angle 4$ $\cong$ $\angle 5$ .	Transitive Property of Congruence

Lines j and k are cut by transversal v, with j

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing statement in step 3 of the two-column proof.

Statement	Reason
1.j $\parallel$ k, and v is a transversal of j and k.	Given
2. $\angle 4$ $\cong$ $\angle 8$ .	Corresponding Angles Postulate
3.	Vertical Angles Theorem
4. $\angle 4$ $\cong$ $\angle 5$ .	Transitive Property of Congruence

Lines l and m are cut by transversal t, with l

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing statement in step 1 of the two-column proof.

Statement	Reason
1.	Given
2. $\angle 4$ $\cong$ $\angle 8$ .	Corresponding Angles Postulate
3. $\angle 8$ $\cong$ $\angle 5$ .	Vertical Angles Theorem
4. $\angle 4$ $\cong$ $\angle 5$ .	Transitive Property of Congruence

Lines l and m are cut by transversal t, with l

\parallel

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

\angle 3

\cong

\angle 6

(a pair of alternate interior angles). Complete the missing statement in step 1 of the two-column proof.

Statement	Reason
1.	Given
2. $\angle 3$ $\cong$ $\angle 7$ .	Corresponding Angles Postulate
3. $\angle 7$ $\cong$ $\angle 6$ .	Vertical Angles Theorem
4. $\angle 3$ $\cong$ $\angle 6$ .	Transitive Property of Congruence

Lines p and q are cut by transversal n, with p

\parallel

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

\angle 3

\cong

\angle 6

(a pair of alternate interior angles). Complete the missing reason in step 3 of the two-column proof.

Statement	Reason
1.p $\parallel$ q, and n is a transversal of p and q.	Given
2. $\angle 3$ $\cong$ $\angle 7$ .	Corresponding Angles Postulate
3. $\angle 7$ $\cong$ $\angle 6$ .
4. $\angle 3$ $\cong$ $\angle 6$ .	Transitive Property of Congruence

Lines j and k are cut by transversal v, with j

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing reason in step 2 of the two-column proof.

Statement	Reason
1.j $\parallel$ k, and v is a transversal of j and k.	Given
2. $\angle 4$ $\cong$ $\angle 8$ .
3. $\angle 8$ $\cong$ $\angle 5$ .	Vertical Angles Theorem
4. $\angle 4$ $\cong$ $\angle 5$ .	Transitive Property of Congruence

Lines l and m are cut by transversal t, with l

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing reason in step 3 of the two-column proof.

Statement	Reason
1.l $\parallel$ m, and t is a transversal of l and m.	Given
2. $\angle 4$ $\cong$ $\angle 8$ .	Corresponding Angles Postulate
3. $\angle 8$ $\cong$ $\angle 5$ .
4. $\angle 4$ $\cong$ $\angle 5$ .	Transitive Property of Congruence

10.

Lines p and q are cut by transversal n, with p

\parallel

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

\angle 4

\cong

\angle 5

(a pair of alternate interior angles). Complete the missing statement in step 1 of the two-column proof.

Statement	Reason
1.	Given
2. $\angle 4$ $\cong$ $\angle 8$ .	Corresponding Angles Postulate
3. $\angle 8$ $\cong$ $\angle 5$ .	Vertical Angles Theorem
4. $\angle 4$ $\cong$ $\angle 5$ .	Transitive Property of Congruence

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