Question

Theorem 2: In a parallelogram, opposite sides are equal

Prove that​

Answer 1

Answer:

Restatement: ABCD is a parallelogram

To prove: AB = DC ( opposite sides of a parallelogram)

and AD = BC ( opposite sides of a parallelogram )

Construction: We join AC

Proof: In triangle ABC and triangle ADC

AB is parallel to CD , AC is the transversal

angle BAC = angle ACD ( alternate angles )

AD is parallel to BC , AC is the transversal

angle DAC = angle BCA ( alternate angles)

AC = AC ( common side )

Therefore, triangle ABC is congruent with triangle ADC (ASA)

Therefore AB = CD (CPCT)

AD = BC (CPCT)