Question

Which segments are parallel? Select each correct answer.

AB
CD
GH
EF

Answer 1

AB ║ CD

AB ║ EF

Explanation:

For line segments AB and CD,

In the figure attached,

m∠IAB = 42° and m∠IDC = 42°

Therefore, ∠IAB = ∠IDC

These angles are formed by line segments AB, CD and a transverse AD, and these angles are the alternate angles.

Therefore, the line segments AB and CD are parallel.

For Line segments GH and EF,

If EF and GH are parallel and AD is a transverse, ∠FEI should be equal to ∠IHG [ Alternate angles]

But m∠FEI = 180° - 138°

= 42°

and m∠IHG = 180° - 122°

= 58°

Therefore, ∠IHG ≠ ∠FEI

Therefore, line segments EF and GH are not parallel.

For AB and EF,

If these segments are parallel then m∠EAB + m∠AEF = 180° [Internal angles formed by parallel lines and a transverse AD]

Since m∠EAB = 42° and m∠AEF = 138°

Therefore, 42° + 138° = 180°

Which proves that Line segments AB and EF are parallel.

For line segments GH and CD

If GH and CD are parallel then m∠CDH + m∠GHD = 180° [[Internal angles formed by parallel lines GH and CD and a transverse AD]

Given, m∠CDH = 42° and m∠GHD = 122°

Therefore, m∠CDH + m∠GHD = 42° + 122° = 164°

Which shows line segments GH and CD are not parallel.

Answer 2

AB, EF, and CD.

Explanation:

I used the answer before me on this question and I ended up getting it wrong. Here's the right answer for this question to make this question less confusing.