(C) In $\triangle ADC$,the exterior angle $\angle ADB$ is greater than the interior opposite angle $\angle DAC$.Since $AD$ is the bisector of $\angle

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(C) In $\triangle ADC$,the exterior angle $\angle ADB$ is greater than the interior opposite angle $\angle DAC$.Since $AD$ is the bisector of $\angle BAC$,we have $\angle BAD = \angle DAC$.Substituting this into the inequality,we get $\angle ADB > \angle BAD$.In $\triangle ABD$,since the side opposite to the greater angle is longer,we have $AB > BD$.

Class 9 Mathematics Triangles Mix Examples - Triangles

Easy

$D$ is a point on the side $BC$ of a $\triangle ABC$ such that $AD$ bisects $\angle BAC$. Then

A
$BD = CD$
B
$BD > BA$
C
$BA > BD$
D
$CD > CA$

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Mix Examples - Triangles

In triangles $ABC$ and $PQR$,$AB = AC$,$\angle C = \angle P$ and $\angle B = \angle Q$. The two triangles are

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In the given figure,$AB \perp BQ$,$PQ \perp QB$,$AC = PR$ and $BR = QC$. Prove that $\angle BAC = \angle QPR$.

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If $\Delta XYZ$ has $XY = 7 \, cm$ and $YZ = 10 \, cm$,the perimeter of $\Delta XYZ$ is greater than how many centimeters?

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In the given figure,$XP = XS$,$XQ = XR$ and $\angle PXR = \angle SXQ$. Prove that $PQ = SR$.

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In $\Delta ABC$,$AB = AC$ and $AD$ is an altitude to the base $BC$. Prove that $D$ is the midpoint of $BC$.

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$D$ is a point on the side $BC$ of a $\triangle ABC$ such that $AD$ bisects $\angle BAC$. Then

Similar Questions

In triangles $ABC$ and $PQR$,$AB = AC$,$\angle C = \angle P$ and $\angle B = \angle Q$. The two triangles are

In the given figure,$AB \perp BQ$,$PQ \perp QB$,$AC = PR$ and $BR = QC$. Prove that $\angle BAC = \angle QPR$.

If $\Delta XYZ$ has $XY = 7 \, cm$ and $YZ = 10 \, cm$,the perimeter of $\Delta XYZ$ is greater than how many centimeters?

In the given figure,$XP = XS$,$XQ = XR$ and $\angle PXR = \angle SXQ$. Prove that $PQ = SR$.

In $\Delta ABC$,$AB = AC$ and $AD$ is an altitude to the base $BC$. Prove that $D$ is the midpoint of $BC$.

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