# Side AB of parallelogram ABCD is twice as large as side AD. Point K is the midpoint of side AB. Prove that DK is an ADC angle bisector

May 31, 2020 | Education

| Consider the triangle AKD.

AK = AD (by the condition of the problem), therefore this triangle is isosceles.

By the property of an isosceles triangle ∠ADK = ∠AKD

∠AKD = ∠KDC (as these are cross-angles).

It turns out that ∠ADK = ∠AKD = ∠KDC.

Therefore, DK is a bisector.

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