In the following figure - ABD - BDC and - CBD - ADB- Then- ABCD is aA- triangleB- parallelogramC- pentagonD- hexagon

The correct option is B parallelogram∠ABD = nbsp;∠BDC (Alternate interior angles) ⇒ AB || CD, BD is the transversal. ∠CBD = nbsp;∠ADB (Alternate interior ...

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Standard VII

Mathematics

Parallelograms

In the follow...

Question

In the following figure $∠$ ABD = $∠$ BDC and $∠$ CBD = $∠$ ADB. Then, ABCD is a __________.

triangle

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parallelogram

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pentagon

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hexagon

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Solution

The correct option is B parallelogram
$∠$ ABD = $∠$ BDC (Alternate interior angles)
$\Rightarrow$ AB || CD, BD is the transversal.

$∠$ CBD = $∠$ ADB (Alternate interior angles)
$\Rightarrow$ AD || BC, BD is the transversal.

$\Rightarrow$ Two pairs of opposite sides are parallel. The figure is a parallelogram.

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In the following figure ∠ABD = ∠BDC and ∠CBD = ∠ADB. Then, ABCD is a __________.

The correct option is B parallelogram∠ABD = ∠BDC (Alternate interior angles) ⇒ AB || CD, BD is the transversal. ∠CBD = ∠ADB (Alternate interior angles) ⇒ AD || BC, BD is the transversal. ⇒ Two pairs of opposite sides are parallel. The figure is a parallelogram.

In the following figure $∠$ ABD = $∠$ BDC and $∠$ CBD = $∠$ ADB. Then, ABCD is a __________.