Answer:
AB ║ CD
AB ║ EF
Step-by-step 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.
