Chapter 1.2, Problem 7PSA

a.

To determine

To Find: Which angle appears to have the same measure as $\angle 1$ .

Answer to Problem 7PSA

  $\angle 1=\angle 5$

Explanation of Solution

Given:

  

Two parallel lines are intersected by a transversal.

Concept Used:

When two parallel lines are intersected by a transversal. Then

1. Alternate interior angles are equal
2. Corresponding angles are equal
3. Vertically opposite angles are equal.

Calculation:

Using the given concept, we can say that

  $\angle 1=\angle 5$

Conclusion:

  $\angle 1=\angle 5$

b.

To determine

To Find: Which angle appears to be larger $\angle 2\text{or }\angle 3$ .

Answer to Problem 7PSA

Both angle are equal.

Explanation of Solution

Given:

  

Two parallel lines are intersected by a transversal.

Concept Used:

When two parallel lines are intersected by a transversal. Then

4. Alternate interior angles are equal
5. Corresponding angles are equal
6. Vertically opposite angles are equal.

Calculation:

Using the given concept, we can say that

  $\angle 2=\angle 3\left(\because \text{Vertically opposite angles are equal}\right)$

So, no two angles $\angle 2\text{or }\angle 3$ are greater between their comparison.

Conclusion:

No two angles $\angle 2\text{or }\angle 3$ are greater between their comparison.

c.

To determine

To Find: Whether $\angle 3$ appears to be congruent to $\angle 4\text{or to }\angle 5$ .

Answer to Problem 7PSA

  $\angle 3$ appears to be congruent to $\angle 4\text{but not to }\angle 5$ .

Explanation of Solution

Given:

  

Two parallel lines are intersected by a transversal.

Concept Used:

When two parallel lines are intersected by a transversal. Then

7. Alternate interior angles are equal
8. Corresponding angles are equal
9. Vertically opposite angles are equal.

Calculation:

Using the given concept, we can say that

  $\begin{array}{l}\angle 3=\angle 4\left(\because \text{Corresponding angles are equal}\right)\\ \text{But, }\angle 3\ne \angle 5\end{array}$

Conclusion:

  $\angle 3=\angle 4$