Question

Theorem 8.2 : In a parallelogram, opposite sides are equal.
You have already proved that a diagonal divides the parallelogram into two congruent. plz prove this theorem.​

Answer 1

Answer:

Hello mate!!

Step-by-step explanation:

Plzz refrence to the above picture

Answer 2

AB = CD  and AD = BC (by cpct )

Step-by-step explanation:

since , It is proved that the diagonals of a parallelogram divide the parallelogram into two congruent. triangles

then

to prove : In a parallelogram, opposite sides are equal.

proof : opposite sides of a parallelogram are parallel

so

AB ║ CD

AD ║ BC

since , AB ║ CD and AC is a transversal

then $\angle BAC = \angle DCA$ (alternate angles )

similarly

$\angle DAC = \angle BCA$

In triangle ABC and ADC

$\angle BAC = \angle DCA$

AC = AC (common)

$\angle DAC = \angle BCA$

therefore ,

$\bigtriangleup ABC \cong \bigtriangleup ADC$

Hence,

AB = CD  and AD = BC (by cpct )

hence proved

#Learn more:

If the adjacent sides of a parallelogram are equal then the parallelogram is a

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