Common Core Geometry, January 2015, Question 32
32. In the diagram below, EF intersects AB and CD at G and H, respectively, and GI is drawn such that GH = IH.
If m<EGB = 50o and m<DIG = 115o, explain why AB||CD.
Angle HIG is supplementary to DIG, which is 115 degrees. This makes HIG 65 degrees.
Angles HIG and IGH are congruent because they are base angles of an isosceles triangle (GH = IH). This means that IGH is also 65 degrees.
Angle GHI is 50 because a triangle has 180 degrees, and 180 - 65 - 65 = 50 degrees
Corresponding angles GHI and EGB are congruent so AB || CD.
Look at the image below:
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