Question

Prove that oposite angles of parallelogram are equal

Answer 1

Solution:

Given:

Prove that oposite angles of parallelogram are equal.

Step-by-step:

A parallelogram ABCD

AC = diagonal.

To prove:

Angle A = Angle C.

Angle B = Angle D.

Proof:

Opposite sides of parallelogram is parallel.

AB || DC and AD || BC

Since AB || DC:

AC = transveral.

Angle BAC = Angle DCA – Equation(1)

Since AD || BC:

AC = transveral.

Angle DAC = Angle BCA – Equation(2)

Adding both equation (1) and (2):

Angle BAC + Angle DAC = Angle DCA + Angle BCA.

Angle BAD = Angle DCB

Prove:

Angle ADC = Angle ABC

Therefore, Proved!!!

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Answer 2

Answer:

A parallelogram ABCD

AC = diagonal

Prove

Angle A = Angle C

Angle B = Angle D

Proof

Opposite sides of parallelogram is parallel.

AB|| DC and AD || BC

Since AD || BC

AC = Transveral

Angle DAC = Angle DCA – Equation (1)

Since AD || BC

AC = Transveral

Angle DAC = Angle BCA – Equation (2)

Adding both Equation (1) and (2)

Angle BAC + Angle DAC = Angle DCA + Angle BCA

Angle BAD = Angle DCB

Prove

Angle ADC = Angle ABC

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