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 lines. Corresponding angles are in the same relative position. 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: Answer question 9

a)

The transversal is line \(l\) as it intersects lines \(j\) and \(k\).

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 \(\angle8\)

Step3: Answer question 10

a)

The transversal connecting \(\angle1\) and \(\angle5\) is \(p\).

b)

The transversal connecting \(\angle7\) and \(\angle14\) is \(q\).

c)

The transversal connecting \(\angle8\) and \(\angle11\) is \(p\).

d)

The transversal connecting \(\angle6\) and \(\angle15\) is \(q\).

e)

The transversal connecting \(\angle3\) and \(\angle9\) is \(p\).

Step4: Answer question 11

a)

\(\angle4\) and \(\angle7\): none (they are vertical angles)

b)

\(\angle2\) and \(\angle11\): alternate - exterior angles

c)

\(\angle6\) and \(\angle16\): corresponding angles

d)

\(\angle8\) and \(\angle13\): alternate - interior angles

e)

\(\angle11\) and \(\angle15\): consecutive - interior angles

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 \(\angle10\): corresponding angles

n)

\(\angle8\) and \(\angle14\): none

Answer:

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