Question

What is the reason for the third step in this proof?

Given: a || b, and both lines are cut by transversal t.

Pls. see attachment.

Answer 1

The correct reason for number 3 is the Alternate Interior Angle.

Alternate Interior Angles are a pair of angles on the alternate sides of a transversal and they are on the interior of two crossed lines. Another example of a pair of Alternate Interior Angles are angles ∠4 and ∠5.

Answer 2

Step: 3
`\angle 3\cong\angle 6`

Reason:Alternate interior angles theorem.

Explanation:

We are given that

`a\parallel b` and both lines are cut by transversal t.

We have to find third step in proof.

Proof:

Step 1:
`a\parallel b`

Reason :Given

Step 2:
`\angle 2\cong\angle 3`

Reason: Verticale angles theorem.

Step: 3
`\angle 3\cong\angle 6`

Reason:Alternate interior angles theorem.

Step 4:
`\angle 2\cong\angle 6`

Reason: Transitive property of congruence

Step 5:
`\angle 6\cong\angle 7`

Reason:Vertical angles theorem

Step 6:
`\angle 2\cong\angle 7`

Reason:Transitive property of congruence.

Hence, proved