(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 Mix Examples - 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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Mix Examples - Triangles

In rectangle $ABCD$,$AB^{2} + BC^{2} + CD^{2} + DA^{2} = 338$,then $AC = \ldots$

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$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow ZXY$. If $AB = 12, BC = 8, CA = 10$ and $ZX = 10$,then $XY + YZ = \ldots$

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In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$BD = 9$ and $BC = 21$,find $AC$.

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In quadrilateral $ABCD$,$P$ is the midpoint of $\overline{BC}$. If $\overline{DP}$ produced intersects $\overline{AB}$ produced at $Q$,prove that $AB = 2CD$ given that $ABCD$ is a parallelogram.

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In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AB = 2\sqrt{10}$ and $AM = 5$,find $CM$.

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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 rectangle $ABCD$,$AB^{2} + BC^{2} + CD^{2} + DA^{2} = 338$,then $AC = \ldots$

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow ZXY$. If $AB = 12, BC = 8, CA = 10$ and $ZX = 10$,then $XY + YZ = \ldots$

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$BD = 9$ and $BC = 21$,find $AC$.

In quadrilateral $ABCD$,$P$ is the midpoint of $\overline{BC}$. If $\overline{DP}$ produced intersects $\overline{AB}$ produced at $Q$,prove that $AB = 2CD$ given that $ABCD$ is a parallelogram.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AB = 2\sqrt{10}$ and $AM = 5$,find $CM$.

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