(C) Given the ratio of sides: $\frac{PQ}{YZ} = \frac{QR}{XZ} = \frac{RP}{XY}$.By the $SSS$ (Side-Side-Side) similarity criterion,the correspondence mu

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(C) Given the ratio of sides: $\frac{PQ}{YZ} = \frac{QR}{XZ} = \frac{RP}{XY}$.By the $SSS$ (Side-Side-Side) similarity criterion,the correspondence must match the vertices in the order of the sides.Comparing the sides:$PQ$ corresponds to $YZ$$QR$ corresponds to $ZX$$RP$ corresponds to $XY$Thus,the vertices $P, Q, R$ correspond to $Y, Z, X$ respectively.Therefore,$\Delta PQR \sim \Delta YZX$.

Class 10 Mathematics Triangles Criteria for Similarity of Triangles

Medium

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

A
$\Delta PQR \sim \Delta XYZ$
B
$\Delta PQR \sim \Delta ZYX$
C
$\Delta PQR \sim \Delta YZX$
D
$\Delta PQR \sim \Delta XZY$

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Triangles

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Criteria for Similarity of Triangles

If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow DEF$,and $2 m \angle X = 3 m \angle Y$ with $m \angle Z = 30^{\circ}$,find $m \angle E$. (in $^{\circ}$)

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In the figure,$D$ is a point on the hypotenuse $AC$ of $\Delta ABC,$ such that $BD \perp AC,$ $DM \perp BC,$ and $DN \perp AB.$ Prove that $DM^{2} = DN \cdot MC.$

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In $\Delta ABC$ and $\Delta PQR$,$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$. If $AB = 15$,$PQ = 20$ and $BC = 12$,find $QR$.

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In the figure,$ABC$ and $DBC$ are two triangles on the same base $BC$. If $AD$ intersects $BC$ at $O$,show that $\frac{\operatorname{ar}(ABC)}{\operatorname{ar}(DBC)} = \frac{AO}{DO}$.

Difficult

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In the figure,$\Delta ABC$ and $\Delta AMP$ are two right-angled triangles,right-angled at $B$ and $M$ respectively. Prove that:
$(i)$ $\Delta ABC \sim \Delta AMP$
$(ii)$ $\frac{CA}{PA} = \frac{BC}{MP}$

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?

Similar Questions

If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow DEF$,and $2 m \angle X = 3 m \angle Y$ with $m \angle Z = 30^{\circ}$,find $m \angle E$. (in $^{\circ}$)

In the figure,$D$ is a point on the hypotenuse $AC$ of $\Delta ABC,$ such that $BD \perp AC,$ $DM \perp BC,$ and $DN \perp AB.$ Prove that $DM^{2} = DN \cdot MC.$

In $\Delta ABC$ and $\Delta PQR$,$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$. If $AB = 15$,$PQ = 20$ and $BC = 12$,find $QR$.

In the figure,$ABC$ and $DBC$ are two triangles on the same base $BC$. If $AD$ intersects $BC$ at $O$,show that $\frac{\operatorname{ar}(ABC)}{\operatorname{ar}(DBC)} = \frac{AO}{DO}$.

In the figure,$\Delta ABC$ and $\Delta AMP$ are two right-angled triangles,right-angled at $B$ and $M$ respectively. Prove that:$(i)$ $\Delta ABC \sim \Delta AMP$$(ii)$ $\frac{CA}{PA} = \frac{BC}{MP}$

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In the figure,$\Delta ABC$ and $\Delta AMP$ are two right-angled triangles,right-angled at $B$ and $M$ respectively. Prove that:
$(i)$ $\Delta ABC \sim \Delta AMP$
$(ii)$ $\frac{CA}{PA} = \frac{BC}{MP}$