Question

Prove that a diagonal of a parallelogram divide it into two congruent triangles?




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Answer 1

Step-by-step explanation:

Parallelogram = ABCD. Diagonal = AC.

To Prove: Diagonal of a parallelogram divides it into two congruent triangles.

Solution: In ΔABC and ΔACD. AB || CD and AC is a transversal. Thus, ∠ ACB = ∠ CAD. AC = AC (common side) ∠CAB = ∠ ACD. Thus, by ASA congruency ΔABC ≅ ΔACD.

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Answer 2

Answer:

Parallelogram = ABCD. Diagonal = AC.

To Prove: Diagonal of a parallelogram divides it into two congruent triangles.

Solution: In ΔABC and ΔACD. AB || CD and AC is a transversal. Thus, ∠ ACB = ∠ CAD. AC = AC (common side) ∠CAB = ∠ ACD. Thus, by ASA congruency ΔABC ≅ ΔACD.