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 definitions

A transversal is a line that intersects two or more other lines. Corresponding angles are in the same relative position, alternate - interior angles are between the two intersected lines and on opposite sides of the transversal, alternate - exterior angles are outside the two intersected lines and on opposite sides of the transversal, consecutive - interior angles are between the two intersected lines and on the same side of the transversal, and consecutive - exterior angles are outside the two intersected lines and on the same side of the transversal.

Step2: Answer question 9

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

Step3: Answer question 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 \(p\).

Step4: Answer question 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 \(\angle15\): Alternate - interior angles.
f. \(\angle7\) and \(\angle10\): None.
g. \(\angle9\) and \(\angle14\): None.
h. \(\angle12\) and \(\angle15\): Consecutive - interior angles.
i. \(\angle6\) and \(\angle7\): None.
j. \(\angle1\) and \(\angle3\): None.
k. \(\angle14\) and \(\angle16\): Consecutive - interior angles.
l. \(\angle6\) and \(\angle15\): None.
m. \(\angle5\) and \(\angle10\): Corresponding angles.
n. \(\angle8\) and \(\angle14\): Alternate - exterior angles.

Answer:

9a. Line \(t\)
9b. \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\)
9c. \(\angle3\) and \(\angle5\), \(\angle4\) and \(\angle6\)
9d. \(\angle1\) and \(\angle7\), \(\angle2\) and \(\angle8\)
9e. \(\angle3\) and \(\angle6\), \(\angle4\) and \(\angle5\)
9f. \(\angle1\) and \(\angle8\), \(\angle2\) and \(\angle7\)
10a. Line \(p\)
10b. Line \(q\)
10c. Line \(p\)
10d. Line \(q\)
10e. Line \(p\)
11a. Alternate - interior angles
11b. None
11c. Corresponding angles
11d. None
11e. Alternate - interior angles
11f. None
11g. None
11h. Consecutive - interior angles
11i. None
11j. None
11k. Consecutive - interior angles
11l. None
11m. Corresponding angles
11n. Alternate - exterior angles