Question

prove that opposite angles of ||gm are equal​

Answer 1

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Prove that opposite angles of ||gm are equal.

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Answer 2

ANSWER

Here, ABCD is a parallelogram with AC as its diagonal.

We know, in parallelogram opposites sides are parallel.

So, AB∥DC and AD∥BC

Since, AB∥DC and AC is the transversal

⇒ ∠BAC=∠DCA ---- ( 1 ) [ Alternate angles ]

Similarly, AD∥BC and AC is the transversal.

⇒ ∠DAC=∠BCA ---- ( 2 ) [ Alternate angles ]

Adding ( 1 ) and ( 2 ),

⇒ ∠BAC+∠DAC=∠DCA+∠BCA

⇒ ∠BAD=∠DCB

Similarly, we can prove, ∠ADC=∠ABC.

∴ We have proved that, opposite angles of a parallelogram are equal......

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