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Sambhaji Maharaj

If ABCD is a ...

Question

If ABCD is a parallelogram with AB || CD, AD || BC, and BD is the diagonal, then the $△ A B D$ and $△ B C D$ are always .

equilateral

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isoceles

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scalene

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congruent

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Solution

The correct option is D congruent

Given a parallelogram ABCD.

Consider $△ A B D$ and $△ B C D$ .
$A B = C D$ (Opposite sides of a parallelogram are equal)
$B D = B D$ (Common Side)
$∠ A B D = ∠ B D C$ (Alternate interior angles)

By SAS congruence criterion, the two triangles are congruent.

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Similar questions

Construct a parallelogram ABCD, if :

(i) AB = 3.6 cm, BC = 4.5 cm and $∠ ABC = 120^{\circ} .$

(ii) BC = 4.5 cm, CD = 5.2 cm and $∠ ADC = 75^{\circ} .$

(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.

(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.

(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is $75^{\circ}$ .

(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is $45^{\circ}$ .

(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is $60^{\circ}$ .

△ A B D

△ B C D

△ A B D

△ B C D

A B C D

A B | | C D

A D = B C

A C

B D

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