(A) In $\Delta ABC$,$m \angle B = 90$ and $D$ is the midpoint of the hypotenuse $\overline{AC}$.According to the theorem of the median to the hypotenu

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(A) In $\Delta ABC$,$m \angle B = 90$ and $D$ is the midpoint of the hypotenuse $\overline{AC}$.According to the theorem of the median to the hypotenuse in a right-angled triangle,the length of the median to the hypotenuse is half the length of the hypotenuse.Therefore,$BD = \frac{1}{2} AC$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Easy

In $\Delta ABC$,$m \angle B = 90$ and $D$ is the midpoint of $\overline{AC}$. Then,$BD = \dots$

A
$\frac{1}{2} AC$
B
$AB$
C
$BC$
D
$AD \cdot DC$

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Mix Examples - Triangles

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $QM = 6$ and $MR = 9$,then $PR = \ldots$

Medium

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In $\Delta PQR$ and $\Delta XYZ$,$\frac{PQ}{YZ} = \frac{QR}{XZ} = \frac{RP}{XY}$. Which correspondence between them is a similarity?

Medium

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In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$AC = 8$ and $BD = 9$,find $DC$.

Medium

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In $\Delta ABC$,if $\ldots \ldots \ldots \ldots$,then by Apollonius' theorem,$AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$ holds good.

Easy

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In $\triangle ABC$,$AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$. Is this triangle a right triangle? Give reasons for your answer.

Medium

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In $\Delta ABC$,$m \angle B = 90$ and $D$ is the midpoint of $\overline{AC}$. Then,$BD = \dots$

Similar Questions

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $QM = 6$ and $MR = 9$,then $PR = \ldots$

In $\Delta PQR$ and $\Delta XYZ$,$\frac{PQ}{YZ} = \frac{QR}{XZ} = \frac{RP}{XY}$. Which correspondence between them is a similarity?

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$AC = 8$ and $BD = 9$,find $DC$.

In $\Delta ABC$,if $\ldots \ldots \ldots \ldots$,then by Apollonius' theorem,$AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$ holds good.

In $\triangle ABC$,$AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$. Is this triangle a right triangle? Give reasons for your answer.

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