Class 10 Mathematics Triangles Textbook - Triangles

Easy

State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

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Solution

(NONE) In $\triangle LMP$ and $\triangle DEF$:
$\frac{LM}{DE} = \frac{2.7}{4} = 0.675$
$\frac{LP}{DF} = \frac{3}{6} = 0.5$
$\frac{MP}{EF} = \frac{2}{5} = 0.4$
Since the ratios of the corresponding sides are not equal (i.e.,$\frac{LM}{DE} \neq \frac{LP}{DF} \neq \frac{MP}{EF}$),the two triangles are not similar.

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$S$ and $T$ are points on sides $PR$ and $QR$ of $\Delta PQR$ such that $\angle P = \angle RTS$. Show that $\Delta RPQ \sim \Delta RTS$.

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$ABCD$ is a trapezium with $AB \parallel DC.$ $E$ and $F$ are points on non-parallel sides $AD$ and $BC$ respectively such that $EF \parallel AB$ (see Figure). Show that $\frac{AE}{ED} = \frac{BF}{FC}$.

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$ABCD$ is a trapezium in which $AB \parallel DC$ and its diagonals intersect each other at the point $O$. Show that $\frac{AO}{BO} = \frac{CO}{DO}$.

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In the figure,altitudes $AD$ and $CE$ of $\Delta ABC$ intersect each other at the point $P$. Show that $\Delta AEP \sim \Delta ADB$.

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In the figure,$O$ is a point in the interior of a triangle $ABC$,$OD \perp BC$,$OE \perp AC$,and $OF \perp AB$. Show that $AF^{2} + BD^{2} + CE^{2} = AE^{2} + CD^{2} + BF^{2}$.

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State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

Similar Questions

$S$ and $T$ are points on sides $PR$ and $QR$ of $\Delta PQR$ such that $\angle P = \angle RTS$. Show that $\Delta RPQ \sim \Delta RTS$.

$ABCD$ is a trapezium with $AB \parallel DC.$ $E$ and $F$ are points on non-parallel sides $AD$ and $BC$ respectively such that $EF \parallel AB$ (see Figure). Show that $\frac{AE}{ED} = \frac{BF}{FC}$.

$ABCD$ is a trapezium in which $AB \parallel DC$ and its diagonals intersect each other at the point $O$. Show that $\frac{AO}{BO} = \frac{CO}{DO}$.

In the figure,altitudes $AD$ and $CE$ of $\Delta ABC$ intersect each other at the point $P$. Show that $\Delta AEP \sim \Delta ADB$.

In the figure,$O$ is a point in the interior of a triangle $ABC$,$OD \perp BC$,$OE \perp AC$,and $OF \perp AB$. Show that $AF^{2} + BD^{2} + CE^{2} = AE^{2} + CD^{2} + BF^{2}$.

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