Question

Which lines are parallel? Check all that apply

A: B||F
B: B||D
C: C||E
D: C||D
E: D||F
F: E||F

Answer 1

Options A, C and D

Explanation:

Option A

Angle p = 180° - 89.5° = 90.5° [Linear pair of angles]

If b║f and line a is a transversal line,

m∠p = 90.5° [Alternate exterior angles]

True

Option B

If B║D and line a is a transversal,

m∠q = 89.5° [vertically opposite angles]

∠q + 89.5° = 89.5° + 89.5° = 179°

But angles q and angle with measure 89.5° are the consecutive interior angles and their sum should be 180°.

So the given statement is False.

Option C

c║e

Since, m∠r = 91.5° [Vertically opposite angle]

And m∠r + 89.5° = 180° [Consecutive interior angles]

True.

Option D

c║d

Since, ∠r and ∠q are consecutive interior angles,

m∠r + m∠q = 180°

91.5° + 89.5° = 180°

True

Option E.

d║f

m∠s = 90.5°[Vertically opposite angles]

Since, ∠s and angle with measure 89.5° are the alternate interior angles,

So measure of angle s should be 89.5°.

Therefore, d║f is False.

Option F.

If e║f, angles with measures 89.5° and 90.5° should be equal.

But measures of both are different.

Therefore, e║f is False.

Options A, C and D are the correct options.