Question

Use the photo below:

1. Use the given information to determine which lines, if any, are parallel. Justify each conclusion with a theorem or postulate.

a. ∠8 is supplementary to ∠9.

b. ∠7 ≅ ∠4

c. ∠9 is supplementary to ∠12.

d. ∠9 ≅ ∠11

Answer 1

1. a. If ∠ 8 is supplementary to ∠ 9, then line x and line y are parallel lines whereas line s is the transverse line.

b. ∠ 7 = ∠ 4, gives line x and line y are parallel and line s is the transverse line.

c. ∠ 9 is supplementary to ∠ 12, then line s and line t are parallel and line y is the transverse line.

d. ∠ 9 = ∠ 11 {Alternate angles}

That means line s and line t are parallel and line y is the transverse line.

Explanation:

1. a. If ∠ 8 is supplementary to ∠ 9, then line x and line y are parallel lines whereas line s is the transverse line.

b. ∠ 7 = ∠ 4.

Now, ∠ 7 = ∠ 2 and ∠ 4 = ∠ 9.

So, ∠ 2 = ∠ 9 {Alternate angles}

Hence, line x and line y are parallel and line s is the transverse line.

c. ∠ 9 is supplementary to ∠ 12, then line s and line t are parallel and line y is the transverse line.

d. ∠ 9 = ∠ 11 {Alternate angles}

That means line s and line t are parallel and line y is the transverse line.