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 - diagram, 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 transversals and the intersected lines. For example, in the first diagram, $\angle1$ 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 $\angle16$: Corresponding angles.
d. $\angle8$ and $\angle13$: None.
e. $\angle11$ and $\angle15$: None.
f. $\angle7$ and $\angle10$: None.
g. $\angle9$ and $\angle14$: None.
h. $\angle12$ and $\angle15$: Consecutive - interior angles.
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 - diagram, 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 transversals and the intersected lines. For example, in the first diagram, $\angle1$ 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 $\angle16$: Corresponding angles.
d. $\angle8$ and $\angle13$: None.
e. $\angle11$ and $\angle15$: None.
f. $\angle7$ and $\angle10$: None.
g. $\angle9$ and $\angle14$: None.
h. $\angle12$ and $\angle15$: Consecutive - interior angles.
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.