Chapter 3.2, Problem 2WE

To determine

To find: all the angles congruent to $\angle 1$ if $c\parallel d$ .

Answer to Problem 2WE

  $\angle 6,\angle 9,\angle 14$

Explanation of Solution

Given:

The diagram:

Concept Used:

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

Theorem 2-3: Vertically opposite angles are congruent.

Consider the given figure:

In this figure, by theorem 2-3,

  $\angle 1\cong \angle 6$ (Vertically opposite angles)

Now, lines $c\parallel d$ and a is a transversal, so by postulate 10,

  $\angle 1\cong \angle 9$ (Corresponding angles)

By theorem 2-3,

  $\angle 9\cong \angle 14$ (Vertically opposite angles)

Now, by using the transitive property on $\angle 1\cong \angle 9$ and $\angle 9\cong \angle 14$ .

Thus,

  $\angle 1\cong \angle 14$

Thus, the angles congruent to $\angle 1$ are $\angle 6,\angle 9,\angle 14$ .