Question

Prove: The opposite angles of a parallelogram are equal. ​

Answer 1

Answer:

This proves that opposite angles in any parallelogram are equal. Converse of Theorem 2: If the opposite angles in a quadrilateral are equal, then it is a parallelogram. Given: ∠A=∠C and ∠B=∠D in the quadrilateral ABCD. To Prove: ABCD is a parallelogram.

Step-by-step explanation:

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Answer 2

Given: A parallelogram ABCD in which AB ║ DC and AD ║ BC.

To Prove : Opposite angles are equal

i.e. ∠A = ∠C and ∠B = ∠D

Construction : Draw diagonal AC

Proof : In ∆ABC and ∆CDA : ∠BAC = ∠DCA [Alternate angles]

∠BCA = ∠DAC [Alternate angles]

AC = AC [Common]

∴ ∆ABC ≅ ∆CDA [By ASA]

⇒ ∠B = ∠D [By cpctc] And, ∠BAD = ∠DCB i.e.,

∠A = ∠C

Similarly,

we can prove that ∠B = ∠D

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