Question

Which segments are parallel?

Select each correct answer.
O EF
O AB
O GH
O CD

Answer 1

EF ║ CD and AB ║ CD are the parallel segments.

Explanation:

The given question is incomplete without picture; here is the picture attached with the answer.

Since m∠A = m∠D = 42°

Therefore, AB ║ CD and segment AD is the transverse.

Now ∠AEF + ∠IEF = 180° [Supplementary angles]

138° + ∠IEF = 180°

∠IEF = 180 - 138

= 42°

∠IHG + ∠DHG = 180° [ Supplementary angles ]

∠IHG + 122 = 180

∠IHG = 180 - 122

∠IHG = 58°

But ∠IEF ≠ ∠IHG

Therefore, EF and GH are not parallel.

If the segments AB and GH are parallel then ∠IHG = ∠IAB (By the property of alternate angles)

But ∠IHG ≠ ∠IAB

Therefore, AB and GH are not parallel.

Now ∠IEF ≅ ∠IDC ≅ 42° [alternate angles]

which reveals that EF ║ CD

Therefore, EF ║ CD and AB ║ CD

Answer 2

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