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 lines. In the first - diagram of question 9, line \(l\) intersects lines \(j\) and \(k\), so a transversal is line \(l\).

Step2: Identify corresponding angles

Corresponding angles are in the same relative position. In the first - diagram of question 9, the corresponding angles are \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\).

Step3: Identify alternate interior angles

Alternate interior angles are between the two intersected lines and on opposite sides of the transversal. In the first - diagram of question 9, the alternate interior angles are \(\angle2\) and \(\angle7\), \(\angle3\) and \(\angle6\).

Step4: Identify alternate exterior angles

Alternate exterior angles are outside the two intersected lines and on opposite sides of the transversal. In the first - diagram of question 9, the alternate exterior angles are \(\angle1\) and \(\angle8\), \(\angle4\) and \(\angle5\).

Step5: Identify consecutive interior angles

Consecutive interior angles are between the two intersected lines and on the same side of the transversal. In the first - diagram of question 9, the consecutive interior angles are \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\).

Step6: Identify consecutive exterior angles

Consecutive exterior angles are outside the two intersected lines and on the same side of the transversal. In the first - diagram of question 9, the consecutive exterior angles are \(\angle1\) and \(\angle5\), \(\angle4\) and \(\angle8\).

Step7: Answer question 10 parts

In 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 \(s\).
• d) The transversal connecting \(\angle6\) and \(\angle15\) is \(q\).
• e) The transversal connecting \(\angle3\) and \(\angle9\) is \(p\).

Step8: Classify angle - pairs in question 11

• a. \(\angle4\) and \(\angle7\): none
• b. \(\angle2\) and \(\angle11\): alternate exterior
• c. \(\angle6\) and \(\angle16\): corresponding
• d. \(\angle8\) and \(\angle13\): none
• e. \(\angle11\) and \(\angle15\): none
• f. \(\angle7\) and \(\angle10\): none
• g. \(\angle9\) and \(\angle14\): none
• h. \(\angle12\) and \(\angle15\): corresponding
• i. \(\angle6\) and \(\angle7\): none
• 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:

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. \(s\)
10d. \(q\)
10e. \(p\)
11a. none
11b. alternate exterior
11c. corresponding
11d. none
11e. none
11f. none
11g. none
11h. corresponding
11i. none
11j. none
11k. none
11l. none
11m. none
11n. none