Question

1. use the diagram below to answer the following questions.

c) name all alternate interior angles.
d) name all alternate exterior angles.
e) name all consecutive interior angles.
f) name all consecutive exterior angles.

1. using the diagram below, classify the angle pairs as corresponding, alternate interior, alternate exterior, consecutive interior, consecutive exterior, or none.

a) name the transversal connecting ∠1 and ∠5.
b) name the transversal connecting ∠7 and ∠14.
c) name the transversal connecting ∠8 and ∠11.
d) name the transversal connecting ∠6 and ∠15.
e) name the transversal connecting ∠3 and ∠9.

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position with respect to the transversals and the parallel lines. Alternate interior angles are between the two lines and on opposite sides of the transversal. Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Consecutive interior angles are between the two lines and on the same - side of the transversal. Consecutive exterior angles are outside the two lines and on the same - side of the transversal.

Step2: Analyze question 10

c) Alternate interior angles

Alternate interior angles are non - adjacent angles that lie between two lines and on opposite sides of a transversal. In the given diagram, the alternate interior angles are $\angle2$ and $\angle7$, $\angle3$ and $\angle6$.

d) Alternate exterior angles

Alternate exterior angles are non - adjacent angles that lie outside two lines and on opposite sides of a transversal. In the given diagram, the alternate exterior angles are $\angle1$ and $\angle8$, $\angle4$ and $\angle5$.

e) Consecutive interior angles

Consecutive interior angles are angles that lie between two lines and on the same side of a transversal. In the given diagram, the consecutive interior angles are $\angle3$ and $\angle7$, $\angle2$ and $\angle6$.

f) Consecutive exterior angles

Consecutive exterior angles are angles that lie outside two lines and on the same side of a transversal. In the given diagram, the consecutive exterior angles are $\angle1$ and $\angle5$, $\angle4$ and $\angle8$.

Step3: Analyze question 11

a) $\angle1$ and $\angle5$

The transversal connecting $\angle1$ and $\angle5$ is the line that intersects the two other lines such that $\angle1$ and $\angle5$ are in corresponding positions. They are corresponding angles.

b) $\angle7$ and $\angle14$

The transversal connecting $\angle7$ and $\angle14$ makes them corresponding angles as they are in the same relative position with respect to the transversal and the two lines.

c) $\angle8$ and $\angle11$

The transversal connecting $\angle8$ and $\angle11$ makes them alternate exterior angles as they are outside the two lines and on opposite sides of the transversal.

d) $\angle6$ and $\angle15$

The transversal connecting $\angle6$ and $\angle15$ makes them corresponding angles as they are in the same relative position with respect to the transversal and the two lines.

e) $\angle3$ and $\angle9$

The transversal connecting $\angle3$ and $\angle9$ makes them corresponding angles as they are in the same relative position with respect to the transversal and the two lines.

Answer:

10.
c) $\angle2$ and $\angle7$, $\angle3$ and $\angle6$
d) $\angle1$ and $\angle8$, $\angle4$ and $\angle5$
e) $\angle3$ and $\angle7$, $\angle2$ and $\angle6$
f) $\angle1$ and $\angle5$, $\angle4$ and $\angle8$
11.
a) Corresponding angles
b) Corresponding angles
c) Alternate exterior angles
d) Corresponding angles
e) Corresponding angles