(C) In $\triangle ABC$,$D$ is the mid-point of $AB$ and $E$ is the mid-point of $BC$.According to the Mid-point Theorem,the line segment joining the m

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(C) In $\triangle ABC$,$D$ is the mid-point of $AB$ and $E$ is the mid-point of $BC$.According to the Mid-point Theorem,the line segment joining the mid-points of two sides of a triangle is parallel to the third side and is half of the length of the third side.Therefore,$DE = \frac{1}{2} \times AC$.Given $AC = 7\, cm$.$DE = \frac{1}{2} \times 7\, cm = 3.5\, cm$.

Class 9 Mathematics Quadrilaterals Mix Examples - Quadrilaterals

Medium

In $\triangle ABC$,$AB = 5\, cm$,$BC = 8\, cm$,and $CA = 7\, cm$. If $D$ and $E$ are respectively the mid-points of $AB$ and $BC$,determine the length of $DE$. (in $, cm$)

A
$1.5$
B
$2$
C
$3.5$
D
$4$

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Mix Examples - Quadrilaterals

In $\Delta ABC$,the points $M$ and $N$ are on sides $AB$ and $AC$ respectively such that $AM = \frac{1}{4} AB$ and $AN = \frac{1}{4} AC$. Prove that $MN = \frac{1}{4} BC$.

Medium

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$ABCD$ is a parallelogram. If its diagonals are equal,then find the value of $\angle ABC$. (in $^{\circ}$)

Easy

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In $\Delta ABC$,$P$,$Q$ and $R$ are the midpoints of $AB$,$BC$ and $CA$ respectively,then $\angle BAC = \angle \ldots \ldots \ldots$

Easy

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Prove that in a parallelogram,the bisectors of any two consecutive angles intersect at right angles.

Difficult

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In $\Delta ABC$,$P, Q,$ and $R$ are the midpoints of $AB, BC,$ and $CA$ respectively. Prove that $PBQR, PQCR,$ and $PQRA$ all are parallelograms.

Medium

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In $\triangle ABC$,$AB = 5\, cm$,$BC = 8\, cm$,and $CA = 7\, cm$. If $D$ and $E$ are respectively the mid-points of $AB$ and $BC$,determine the length of $DE$. (in $, cm$)

Similar Questions

In $\Delta ABC$,the points $M$ and $N$ are on sides $AB$ and $AC$ respectively such that $AM = \frac{1}{4} AB$ and $AN = \frac{1}{4} AC$. Prove that $MN = \frac{1}{4} BC$.

$ABCD$ is a parallelogram. If its diagonals are equal,then find the value of $\angle ABC$. (in $^{\circ}$)

In $\Delta ABC$,$P$,$Q$ and $R$ are the midpoints of $AB$,$BC$ and $CA$ respectively,then $\angle BAC = \angle \ldots \ldots \ldots$

Prove that in a parallelogram,the bisectors of any two consecutive angles intersect at right angles.

In $\Delta ABC$,$P, Q,$ and $R$ are the midpoints of $AB, BC,$ and $CA$ respectively. Prove that $PBQR, PQCR,$ and $PQRA$ all are parallelograms.

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