(B) Given that $\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$.By the property of similar triangles,the ratios of their

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(B) Given that $\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$.By the property of similar triangles,the ratios of their corresponding sides are equal:$\frac{XY}{AB} = \frac{YZ}{BC} = \frac{XZ}{AC}$.We are given that $\frac{XY}{AB} = \frac{3}{5}$.Therefore,$\frac{YZ}{BC} = \frac{3}{5}$.To find $\frac{BC}{YZ}$,we take the reciprocal of both sides:$\frac{BC}{YZ} = \frac{5}{3}$.

Class 10 Mathematics Triangles Criteria for Similarity of Triangles

Medium

$\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$. If $\frac{XY}{AB} = \frac{3}{5}$,then $\frac{BC}{YZ} = \dots$

A
$\frac{3}{5}$
B
$\frac{5}{3}$
C
$-\frac{3}{5}$
D
$\frac{7}{3}$

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Triangles

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Criteria for Similarity of Triangles

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 $CM$.

Medium

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In $\Delta PQR$,$\overline{PM}$ is an altitude. If $PM^2 = QM \times RM$,prove that $\Delta PQR$ is a right-angled triangle.

Medium

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............... is not a condition for the similarity of two triangles.

Easy

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In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $BM = 12$,find $AC$.

Medium

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It is given that $\triangle ABC \sim \triangle EDF$ such that $AB = 5 \, cm$,$AC = 7 \, cm$,$DF = 15 \, cm$,and $DE = 12 \, cm$. Find the lengths of the remaining sides of the triangles.

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$\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$. If $\frac{XY}{AB} = \frac{3}{5}$,then $\frac{BC}{YZ} = \dots$

Similar Questions

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 $CM$.

In $\Delta PQR$,$\overline{PM}$ is an altitude. If $PM^2 = QM \times RM$,prove that $\Delta PQR$ is a right-angled triangle.

............... is not a condition for the similarity of two triangles.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $BM = 12$,find $AC$.

It is given that $\triangle ABC \sim \triangle EDF$ such that $AB = 5 \, cm$,$AC = 7 \, cm$,$DF = 15 \, cm$,and $DE = 12 \, cm$. Find the lengths of the remaining sides of the triangles.

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