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: Define transversal

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: Define corresponding angles

Corresponding angles are in the same relative position with respect to the transversal and the intersected lines. For two lines cut by a transversal, if the lines are parallel, corresponding angles are equal.

Step3: Define alternate - interior angles

Alternate - interior angles are between the two intersected lines and on opposite sides of the transversal.

Step4: Define alternate - exterior angles

Alternate - exterior angles are outside the two intersected lines and on opposite sides of the transversal.

Step5: Define consecutive - interior angles

Consecutive - interior angles are between the two intersected lines and on the same side of the transversal.

Step6: Define consecutive - exterior angles

Consecutive - exterior angles are outside the two intersected lines and on the same side of the transversal.

9.

a) In the first diagram, 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 $\angle15$: None.
i. $\angle6$ and $\angle7$: Consecutive - interior angles.
j. $\angle1$ and $\angle3$: None.
k. $\angle14$ and $\angle16$: None.
l. $\angle6$ and $\angle15$: Alternate - exterior angles.
m. $\angle5$ and $\angle10$: None.
n. $\angle8$ and $\angle14$: None.

Answer:

9.

a) Line $l$
b) $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$
c) $\angle2$ and $\angle7$, $\angle3$ and $\angle6$
d) $\angle1$ and $\angle8$, $\angle4$ and $\angle5$
e) $\angle2$ and $\angle6$, $\angle3$ and $\angle7$
f) $\angle1$ and $\angle5$, $\angle4$ and $\angle8$

10.

a) Line $p$
b) Line $q$
c) Line $p$
d) Line $q$
e) Line $p$

11.

a. Alternate - interior angles
b. None
c. Corresponding angles
d. None
e. None
f. None
g. None
h. None
i. Consecutive - interior angles
j. None
k. None
l. Alternate - exterior angles
m. None
n. None