Chapter 3, Problem 23PT

To determine

The theorem that shows the given angle is equal.

Answer to Problem 23PT

Alternate interior angle .

Explanation of Solution

Given:

  

  $\angle 9\cong \angle 6$

Solution:

From the given description,

j and k are parallel lines intersected by a transverse line q.

Then,

By the theorem of Alternate interior angle,

  $\angle 6\cong \angle 10\mathrm{..............}\left(1\right)$

Now,

p and q are parallel lines intersected by a transverse line k.

Then,

By the theorem of Alternate interior angle,

  $\angle 9\cong \angle 10$

Therefore,

From equation 1,

  $\angle 6\cong \angle 10\cong \angle 9$

And,

  $\angle 6\cong \angle 9$

The theorem used is Alternate interior angle.