Question

Show that a diagonal of a parallelogram divides it into two congruent triangles.
(Hint: Use SSS congruence criterion)
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Answer 1

Step-by-step explanation:

Statement : A diagonal of a parallelogram divides it into two congruent triangles.

Given : A parallelogram ABCD.

To prove : ΔBAC ≅ ΔDCA

Construction : Draw a diagonal AC.

Proof :

In ΔBAC and ΔDCA,

∠1 = ∠2 [alternate interior angles]

∠3 = ∠4 [alternate interior angles]

AC = AC [common]

ΔBAC ≅ ΔDCA [ASA]

Hence proved

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Answer 2

Parallelogram Theorem #1:

Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.

Now,

let's prove that if a quadrilateral has opposite sides congruent, then its diagonals divide the quadrilateral into congruent triangles.

• These are the converses of the parallelogram theorems .

Draw a generic quadrilateral with two pairs of congruent sides and preview the proof.

• Your first goal is to show that the set of triangles created by each diagonal must be congruent.

You can use the congruent opposite sides as well as the reflexive property to show that the triangles are congruent with SSS ≅.

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