Question

prove that in a parallelogram ABCD are opposite angle are equal.​

Answer 1

Step-by-step explanation:

Given: Parallelogram ABCD.

To prove: ∠B = ∠D and ∠A=∠C

Proof:

In the parallelogram ABCD,

AB \\ CD and AD \\ BC

Opposite angles of a parallelogram

Consider triangle ABC and triangle ADC,

AC = AC (common side)

We know that alternate interior angles are equal.

∠1 = ∠4

∠2 = ∠3

By ASA congruence criterion, two triangles are congruent to each other.

Therefore, ∠B = ∠D and ∠A=∠C

Hence, it is proved that the opposite angles of a parallelogram are equal.

Consecutive Angles

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.

solution