Question

1. given: ∠5 ≅ ∠6; ∠2 ≅ ∠4

prove: ∠11 and ∠14 are supplementary
1.
2.

1. (overline{cd}paralleloverline{gh})

4.

1. (overline{cd}paralleloverline{ef})
2. ∠11 and ∠14 are supplementary

Explanation:

Step1: Identify given angles

Given \( \angle5\cong\angle6\) and \( \angle2\cong\angle4\).

Step2: Use converse of corresponding angles

Since \( \angle5\cong\angle6\), by the converse of corresponding angles theorem, \( CD\parallel GH\).

Step3: Use converse of alternate - interior angles

Since \( \angle2\cong\angle4\), by the converse of alternate - interior angles theorem, \( CD\parallel EF\).

Step4: Use transitive property of parallel lines

If \( CD\parallel EF\) and \( CD\parallel GH\), then \( EF\parallel GH\).

Step5: Use consecutive - interior angles theorem

Since \( EF\parallel GH\), by the consecutive - interior angles theorem, \( \angle11\) and \( \angle14\) are supplementary.

Answer:

1. \( \angle5\cong\angle6\)
2. \( \angle2\cong\angle4\)
3. Converse of corresponding angles theorem
4. \( EF\parallel GH\)
5. Converse of alternate - interior angles theorem
6. Consecutive - interior angles theorem