with a diagram prove that in a parallelogram opposite sides are equal
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it is a property of parallogram that its opposite sides are equal
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Answered by
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GIVEN: A quadrilateral ABCD in which AB Is equal to DC And AB ||DC.
To prove: ABCD is a ||gm.
Construction: Join A to C
Proof: In triangle ABC and CDA
AB Is equal DC [Given] AC is equal to CA [Common]
and angle BAC is equal to angle DCA [alt.interior angles as AB||DC and CA cuts them]
triangle ABC is congruent to Triangle CDA (SAS criteria)
Angle BCA is equal to angle DAC (c.p.c.t)
But these are alternate interior angles.
AB||BC
Now, AB||DC and AD||BC
HENCE ABCD IS A ||gm.
(You should made Figure yourself)
To prove: ABCD is a ||gm.
Construction: Join A to C
Proof: In triangle ABC and CDA
AB Is equal DC [Given] AC is equal to CA [Common]
and angle BAC is equal to angle DCA [alt.interior angles as AB||DC and CA cuts them]
triangle ABC is congruent to Triangle CDA (SAS criteria)
Angle BCA is equal to angle DAC (c.p.c.t)
But these are alternate interior angles.
AB||BC
Now, AB||DC and AD||BC
HENCE ABCD IS A ||gm.
(You should made Figure yourself)
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