Chapter 3.3, Problem 7ST1

To determine

To identify: two pairs of congruent corresponding interior angles.

Answer to Problem 7ST1

  $\angle 1\cong \angle 5$

  $\angle 2\cong \angle 6$

Explanation of Solution

Given:

The diagram:

Concept Used:

Corresponding angles: These are the two angles which relative to the two lines are in the corresponding position.

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent.

Consider the given figure:

It can be observed that $\angle 1\text{ and }\angle 5$ are in the corresponding position.

Thus, by using the above definitions, it can be said that $\angle 1\text{ and }\angle 5$ are corresponding angles.

Similarly, $\angle 2\text{ and }\angle 6$ are in the corresponding position.

Thus, by using the above definitions, it can be said that $\angle 2\text{ and }\angle 6$ are corresponding angles.

Now it is given that the lines l and m are parallel and the line p is the transversal.

So by Postulate 10, $\angle 1\cong \angle 5$ and $\angle 2\cong \angle 6$ .