Question

Given: AD≅ BC and AD ║ BC Prove: ABCD is a parallelogram. Assemble the proof by bragging tiles to the statements and reasons column.

Answer 1

Explanation:

A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.

Given: parallelogram ABCD

AD≅ BC

AD ║ BC

Thus;

<ABC + DAB =
`180^(o)` (supplementary angle property)

ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)

<ABC = <ADC (both pairs of opposite angles are congruent)

<DAB = <BCD (both pairs of opposite angles are congruent)

AB ≅ CD (opposite sides are congruent)

AB ║ DC (pair of opposite sides are parallel)

Therefore, the quadrilateral ABCD is a parallelogram.