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Answer:
Step-by-step explanation:
by looking at the given image...
the shape ABCD is a parallelogram.
<u>Required:</u>
is to prove ∡A and ∡B are supplementary
and ∡C and ∡D are supplementary.
so, m∠A + m∠B = 180°
and m∠C + m∠D = 180°
<u><em>the Statement </em></u>
1. ABCD is a parallelogram
<em><u>the reason is..</u></em><em> </em>
It is Given!
<u><em>the Statement </em></u>
2.m∠A=m∠C and m∠B=m∠D
<em><u>the reason is..</u></em><em> </em>
Definition of parallelogram.
<u><em>the Statement </em></u>
3.m∠A+m∠B+m∠C+m∠D=360°
<em><u>the reason is..</u></em><em> </em>
Definition of quadrilateral
<u><em>the Statement </em></u>
4. m∠A+m∠B+m∠A+m∠B=360°
<em><u>the reason is..</u></em><em> </em>
By substitution
⇒ 2( m∠A + m∠B ) = 360°
⇒ m∠A + m∠B = 180°
it is also similar m∠C + m∠D = 180°
<u><em>the Statement </em></u>
5.∠A and ∠C are supplementary
<em><u>the reason is..</u></em><em> </em>
by the definition of Supplementary ∠ B and ∠D are supplementary
Hope it helps!
