Question

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

Answer 1

Answer:

Step: 3 $\angle 3\cong\angle 6$

Reason:Alternate interior angles theorem.

Step-by-step 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

Answer 2

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.