Given: ABCD is a parallelogram.
Prove: ∠1 and ∠2 are supplementary.
Proof:
It is given...
Mathematics, 24.01.2021 20:10 kelsea86
Given: ABCD is a parallelogram.
Prove: ∠1 and ∠2 are supplementary.
Proof:
It is given that ABCD is a parallelogram with angles named, in consecutive order, ∠1 , ∠2 , ∠3, and ∠4.
Opposite angles of a parallelogram are congruent. Thus, ∠1=∠3 and ∠2=∠4 by the definition of congruence.
The sum of the interior angles of any quadrilateral is 360°, so ( I )
Using the substitution property, ∠1+∠1+∠2+∠2=360°.
Therefore, 2(∠1+∠2)=360°.
By the division property of equality, ( II )
Therefore, ∠1 and ∠2 are supplementary.
What statements should go in ( I ) and ( II ) of the proof?
Answers: 3
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