Question

In the parallelogram figure, ABCD is a parallelogram. and AC is its diagonal. prove that ⛛ BCA congruent to ⛛ D a. hence prove that, (a) BC=DA (b) AB=CD (c) angle B=angleD

Answer 1

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Answer 2

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$\red{solution}$
: Given =ABCD is a parallelogram,
In which, AB || CD and AC is a diagonal .

Here AB || CD
so, angle BCA = Angle DCA__( alt.interior angles)

And AD || CB,
therefore, angle DAC = BAC ___(alt.int.angles)

TO PROVE = BC=DA , AB = CD ,and angle B = angle D.

PROOF = In triangle ABC & CDA .
Angle BAC = Angle DCA.
and angle BCA = angle DAC.

AC = CA ______ (common sides)

There fore , Triangle ABC is congruent to triangle CDA.

Now, by CPTC

BC=DA
AB=CD

so, angle B = angle D

$\bold{proved}$

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