Question

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

a) name a transversal.
b) name all corresponding angles.
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. use the diagram below to answer the following questions.

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.

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

a. ∠4 and ∠7 b. ∠2 and ∠11
c. ∠6 and ∠16 d. ∠8 and ∠13
e. ∠11 and ∠15 f. ∠7 and ∠10
g. ∠9 and ∠14 h. ∠12 and ∠15
i. ∠6 and ∠7 j. ∠1 and ∠3
k. ∠14 and ∠16 l. ∠6 and ∠15
m. ∠5 and ∠10 n. ∠8 and ∠14

Explanation:

Step1: Recall transversal definition

A transversal is a line that intersects two or more other lines. In the first diagram, line $l$ intersects lines $j$ and $k$. In the second - set of diagrams, lines $p$ and $q$ are transversals to lines $r$ and $s$.

Step2: Recall corresponding - angles definition

Corresponding angles are in the same relative position with respect to the transversal and the intersected lines. For example, in the first diagram with lines $j$, $k$ and transversal $l$, $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$ are corresponding angles.

Step3: Recall alternate - interior - angles definition

Alternate interior angles are between the two intersected lines and on opposite sides of the transversal. In the first diagram, $\angle2$ and $\angle7$, $\angle3$ and $\angle6$ are alternate interior angles.

Step4: Recall alternate - exterior - angles definition

Alternate exterior angles are outside the two intersected lines and on opposite sides of the transversal. In the first diagram, $\angle1$ and $\angle8$, $\angle4$ and $\angle5$ are alternate exterior angles.

Step5: Recall consecutive - interior - angles definition

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

Step6: Recall consecutive - exterior - angles definition

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

9.

a) The transversal is line $l$.
b) Corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.
c) Alternate interior angles: $\angle2$ and $\angle7$, $\angle3$ and $\angle6$.
d) Alternate exterior angles: $\angle1$ and $\angle8$, $\angle4$ and $\angle5$.
e) Consecutive interior angles: $\angle2$ and $\angle6$, $\angle3$ and $\angle7$.
f) Consecutive exterior angles: $\angle1$ and $\angle5$, $\angle4$ and $\angle8$.

10.

a) The transversal connecting $\angle1$ and $\angle5$ is line $p$.
b) The transversal connecting $\angle7$ and $\angle14$ is line $q$.
c) The transversal connecting $\angle8$ and $\angle11$ is line $p$.
d) The transversal connecting $\angle6$ and $\angle15$ is line $q$.
e) The transversal connecting $\angle3$ and $\angle9$ is line $p$.

11.

a. $\angle4$ and $\angle7$: Alternate interior angles.
b. $\angle2$ and $\angle11$: None.
c. $\angle6$ and $\angle16$: None.
d. $\angle8$ and $\angle13$: None.
e. $\angle11$ and $\angle15$: None.
f. $\angle7$ and $\angle10$: None.
g. $\angle9$ and $\angle14$: None.
h. $\angle12$ and $\angle15$: None.
i. $\angle6$ and $\angle7$: Consecutive interior angles.
j. $\angle1$ and $\angle3$: None.
k. $\angle14$ and $\angle16$: None.
l. $\angle6$ and $\angle15$: None.
m. $\angle5$ and $\angle10$: None.
n. $\angle8$ and $\angle14$: None.

Answer:

Step1: Recall transversal definition

A transversal is a line that intersects two or more other lines. In the first diagram, line $l$ intersects lines $j$ and $k$. In the second - set of diagrams, lines $p$ and $q$ are transversals to lines $r$ and $s$.

Step2: Recall corresponding - angles definition

Corresponding angles are in the same relative position with respect to the transversal and the intersected lines. For example, in the first diagram with lines $j$, $k$ and transversal $l$, $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$ are corresponding angles.

Step3: Recall alternate - interior - angles definition

Alternate interior angles are between the two intersected lines and on opposite sides of the transversal. In the first diagram, $\angle2$ and $\angle7$, $\angle3$ and $\angle6$ are alternate interior angles.

Step4: Recall alternate - exterior - angles definition

Alternate exterior angles are outside the two intersected lines and on opposite sides of the transversal. In the first diagram, $\angle1$ and $\angle8$, $\angle4$ and $\angle5$ are alternate exterior angles.

Step5: Recall consecutive - interior - angles definition

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

Step6: Recall consecutive - exterior - angles definition

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

9.

a) The transversal is line $l$.
b) Corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.
c) Alternate interior angles: $\angle2$ and $\angle7$, $\angle3$ and $\angle6$.
d) Alternate exterior angles: $\angle1$ and $\angle8$, $\angle4$ and $\angle5$.
e) Consecutive interior angles: $\angle2$ and $\angle6$, $\angle3$ and $\angle7$.
f) Consecutive exterior angles: $\angle1$ and $\angle5$, $\angle4$ and $\angle8$.

10.

a) The transversal connecting $\angle1$ and $\angle5$ is line $p$.
b) The transversal connecting $\angle7$ and $\angle14$ is line $q$.
c) The transversal connecting $\angle8$ and $\angle11$ is line $p$.
d) The transversal connecting $\angle6$ and $\angle15$ is line $q$.
e) The transversal connecting $\angle3$ and $\angle9$ is line $p$.

11.

a. $\angle4$ and $\angle7$: Alternate interior angles.
b. $\angle2$ and $\angle11$: None.
c. $\angle6$ and $\angle16$: None.
d. $\angle8$ and $\angle13$: None.
e. $\angle11$ and $\angle15$: None.
f. $\angle7$ and $\angle10$: None.
g. $\angle9$ and $\angle14$: None.
h. $\angle12$ and $\angle15$: None.
i. $\angle6$ and $\angle7$: Consecutive interior angles.
j. $\angle1$ and $\angle3$: None.
k. $\angle14$ and $\angle16$: None.
l. $\angle6$ and $\angle15$: None.
m. $\angle5$ and $\angle10$: None.
n. $\angle8$ and $\angle14$: None.