Given: ABCD is a quadrilateral, Segment AB is congruent to Segment CD, <1 is congruent to <2 Prove: ABCD is a parallelogra
1 answer:
Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.
Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.
We need to prove that ABCD is a parallelogram.
<h3>How to prove a given quadrilateral is a parallelogram?</h3>If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.
From the given quadrilateral ABCD:
AB=CD (Given)
∠1=∠2 (Given)
AC=AC (Diagonal)
From ASA congruency ΔABC and ΔADC are congruent.
By CPCT, AD=BC and ∠ABC=∠ADC.
Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.
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8c - 3c + 3 = 13
Begin by combining like terms:
5c + 3 = 13
Subtract 3 from both sides:
5c + 3 - 3 = 13 - 3
5c = 10
Divide both sides by 5:
5c/5 = 10/5
c = 2.