Question

Prove the theorem if in a quadrilateral opposite angles are equal it is a parallelogram

Answer 1

Theorem: If given quadrilateral is parallelogram then it's opposite angles are equal.

Given: Quadrilateral ABCD is a parallelogram. To prove:angleDAB =angleBCD.

Theory: Suppose, quadrilateral ABCD is a parallelogram.

AB || CD and BD is a transversal.

In ∆DAB and ∆BCD,

Angle ABD=Angle BCD____alternate angle.

AB ||CD and AC is a transversal.

In ∆DAB and ∆BCD,

angle BAC=angle ACD_____alternate angle.

BD=DB______common side.

∆DAB=∆BCD______ASA test.

hence,

angle DAB= angle BCD.