Question

Prove that In a parallelogram, opposite angles are equal.

Answer 1

To prove:

a parallelogram, opposite angles are equal.

Given:

AB||CB

DC || AB

AC and DB as transversal

Proof:

AD||CB and AC as transversal ... given

•°•∠DAC = ∠BCA ... Alternate

∠BAC = ∠DCA ... Alternate

•°• ∠BAD = ∠BCA + ∠DCA ..1

DC || AB and DB as transversal

•°• ∠ABD = ∠CDB ..Alternate

∠CBD = ∠ADB ..Alternate

•°• ∠ADC = ∠CBD + ∠ABD ..2

from 1 and 2

•°• ∠DAB = ∠BCD

•°• ∠ADC = ∠ABC

Hence, proved that opposite angles of parallelogram are congruent.