Question

ABCD is a quadrilateral and AC is diagonal . AB = CD and AB parallel CD. Prove that ABC
congruent to ACD.
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Answer 1

Answer:

Given : quadrilateral ABCD

AB = CD

AB parallel CD

To prove : ABC congruent to ACD.

Proof : In triangle ABC and triangle ACD

AB = CD, given

angle CAB = angle ACD , alternative angles are

equal.

AC = AC, command side

Thus, ABC congruent to ACD , by SAS

Congruency criteria.

Hence proved.

Answer 2

Given:

AB || CD

AB = CD

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TO Proove➾

$ABC⩭ACD$

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✏️✒️Proofs⇒

$In \: \Delta ABC \: and \: \Delta ACD$

• AB = CD. (Given)
• AC = AC. (Common)
• <CAB = <DCA. (Alternate Interior Angle)

Therefore,

By

SAS Rule of Congruency ➾

$\Delta ABC ⩭ \Delta ACD$

Hence,

PROOVED✔️✔️