(B) Given that $\angle A = \angle Q$ and $\angle B = \angle R$.By the $AA$ (Angle-Angle) similarity criterion,the triangles are similar if their corre

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(B) Given that $\angle A = \angle Q$ and $\angle B = \angle R$.By the $AA$ (Angle-Angle) similarity criterion,the triangles are similar if their corresponding angles are equal.Since $\angle A$ corresponds to $\angle Q$,$\angle B$ corresponds to $\angle R$,and consequently $\angle C$ must correspond to $\angle P$.Therefore,the correspondence is $\Delta ABC \sim \Delta QRP$.

Class 10 Mathematics Triangles Criteria for Similarity of Triangles

Medium

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle Q$ and $\angle B \cong \angle R$. Which correspondence between them is a similarity?

A
$\Delta ABC \sim \Delta PQR$
B
$\Delta ABC \sim \Delta QRP$
C
$\Delta ABC \sim \Delta RQP$
D
$\Delta ABC \sim \Delta PRQ$

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Class 10

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Triangles

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Criteria for Similarity of Triangles

In the figure,the line segment $XY$ is parallel to side $AC$ of $\Delta ABC$ and it divides the triangle into two parts of equal areas. Find the ratio $\frac{AX}{AB}$.

Medium

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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.

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In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $QR = 9$ and $PR = 13.5$,find $RM$.

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The correspondence $PQR \leftrightarrow ZYX$ between $\Delta PQR$ and $\Delta XYZ$ is a similarity. If $PQ : ZY = 5 : 3$ and $PR = 10$,find $ZX$.

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In $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

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In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle Q$ and $\angle B \cong \angle R$. Which correspondence between them is a similarity?

Similar Questions

In the figure,the line segment $XY$ is parallel to side $AC$ of $\Delta ABC$ and it divides the triangle into two parts of equal areas. Find the ratio $\frac{AX}{AB}$.

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.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $QR = 9$ and $PR = 13.5$,find $RM$.

The correspondence $PQR \leftrightarrow ZYX$ between $\Delta PQR$ and $\Delta XYZ$ is a similarity. If $PQ : ZY = 5 : 3$ and $PR = 10$,find $ZX$.

In $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

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