Question

those give 80Complete the proofs for questions 10-13 using the diagram below. If it cannot be proven, write"cannot prove". Note, you may not use all lines provided.13/1614/1510. Given 316 3410, provej Ilk11. Given 3241: Prove: mlp.StatementReasonStatementReasonhich angles and by which converse would prove lino di

Answer 1

10. Using the converse of the alternate interior angle theorem, we can prove that line J is parallel to line K.

Given:

`\angle\text{ 16 }\cong\text{ }\angle\text{ 10}`

Prove: J || K

Statement:

`\angle\text{ 16 }\cong\text{ }\angle\text{ 10 }`

Reason: Given

Statement:

`\angle\text{ 10 }\cong\text{ }\angle\text{ 12 }`

Reason: Vertical angles theorem

Statement:

`\angle\text{ 12 }\cong\text{ }\angle\text{ 16}`

Reason: Transitive property of congruence

Statement:

J || K

Reason:

`\text{Converse of the corresponding angles postulate}`