ABCD is a quadrilateral in which AB = CD and AD = BC. Diagonal AC is drawn. Which congruence rule proves triangle ABC congruent to triangle CDA, leading to ABCD being a parallelogram?

Question

Accepted Answer

SSS. In triangles ABC and CDA: AB = CD, BC = DA and AC = CA (common). By SSS the triangles are congruent, giving equal alternate angles, so opposite sides are parallel and ABCD is a parallelogram.

ABCD is a quadrilateral in which AB = CD and AD = BC.
Diagonal AC is drawn.
Which congruence rule proves triangle ABC congruent to triangle CDA, leading to ABCD being a parallelogram?

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More Class 9 Conditions for a Parallelogram practice

ABCD is a quadrilateral in which AB = CD and AD = BC.Diagonal AC is drawn.Which congruence rule proves triangle ABC congruent to triangle CDA, leading to ABCD being a parallelogram?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Conditions for a Parallelogram practice

ABCD is a quadrilateral in which AB = CD and AD = BC.
Diagonal AC is drawn.
Which congruence rule proves triangle ABC congruent to triangle CDA, leading to ABCD being a parallelogram?