Please help with Geometry Proofs?

Given Rectangle ABCD, E is the Midpoint of DC

Prove angle 1 is congruent to angle 2

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  • 5 years ago
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    AB//CD. (given)

    And Taking AE as transversal:

    Angle1 = Angle(DEA)

    (alternate interior angles)

    Angle1+Angle(AEC) = 180°

    (corresponding angles)

    Similarly

    Taking BE as transversal:

    Angle2 = Angle (CEB)

    (alternate interior angles)

    Angle2+Angle(BED) = 180°

    (corresponding angles)

    So,

    Angle1+Angle(AEC) = Angle2+Angle(BED)

    Angle1+Angle(AEB+CEB) =

    Angle2+Angle(AEB+DEA)

    2(Angle1) = 2(Angle2)

    => Angle1 = Angle2

    Hence Angle1 and Angle2 are congruent.

    Proved.

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