Detective Reese has now proven that adjacent angles in a parallelogram are supplementary. Use the steps demonstrated by Reese to create your own proof.
Prove that ∠X and ∠Y are supplementary.
Create your proof by placing the following steps in the correct order.
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In parallelogram WXYZ, prove ∠X and ∠Y are supplementary.
∠a° = ∠q° because they are alternate interior angles.
Let ∠W = ∠b° + ∠a° and
let ∠Y = ∠p° + ∠q°. Draw diagonal WY to create △WXY and △WZY.
Since ∠Y = ∠p° + ∠q°, substitute to get ∠X + ∠Y = 180°.
Since ∠a° = ∠q°, substitute to get
∠X + ∠p° + ∠q° = 180°. By the definition of supplementary, ∠X and ∠Y are supplementary.
In △WXY, ∠X + ∠p° + ∠a° = 180°.
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Great job! You got them all!
The ones with X's are incorrect. Try again.
You just proved that adjacent angles in a parallelogram are supplementary.
