Question

prove that opposite angle of a parallgram are equal​

Answer 1

Answer:

Answer:Opposite Angles of a Parallelogram are equal

Answer:Opposite Angles of a Parallelogram are equalGiven: Parallelogram ABCD. We know that alternate interior angles are equal. By ASA congruence criterion, two triangles are congruent to each other. Hence, it is proved that the opposite angles of a parallelogram are equal.

Answer 2

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.