Question

parallel lines & transversals: if two parallel lines are cut, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, consecutive (same - side) interior angle, consecutive (same - side) exterior angle, and recall from unit 1, vertical angles angles that form a linear pair are always. example 1 identify the angle pair as congruent or supplementary. a. ∠3 and ∠5 b. ∠1 and ∠8 c. ∠2 and ∠6 d. ∠1 and ∠7 e. ∠4 and ∠5 f. ∠3 and ∠7 g. ∠5 and ∠6 h. ∠2 and ∠4

Explanation:

Step1: Recall angle - pair properties

When two parallel lines are cut by a transversal, we use the following rules: corresponding angles are congruent, alternate - interior angles are congruent, alternate - exterior angles are congruent, consecutive (same - side) interior angles are supplementary, consecutive (same - side) exterior angles are supplementary, and vertical angles are congruent.

Step2: Analyze each angle - pair

a. $\angle3$ and $\angle5$

They are alternate - interior angles. So, they are congruent.

b. $\angle1$ and $\angle8$

They are alternate - exterior angles. So, they are congruent.

c. $\angle2$ and $\angle6$

They are corresponding angles. So, they are congruent.

d. $\angle1$ and $\angle7$

They are alternate - exterior angles. So, they are congruent.

e. $\angle4$ and $\angle5$

They are consecutive (same - side) interior angles. So, they are supplementary.

f. $\angle3$ and $\angle7$

They are corresponding angles. So, they are congruent.

g. $\angle5$ and $\angle6$

They are vertical angles. So, they are congruent.

h. $\angle2$ and $\angle4$

They are vertical angles. So, they are congruent.

Answer:

a. Congruent
b. Congruent
c. Congruent
d. Congruent
e. Supplementary
f. Congruent
g. Congruent
h. Congruent