(C) In a right-angled triangle $\Delta ABC$ where $\angle B = 90^{\circ}$,if $\overline{BM}$ is the altitude to the hypotenuse $AC$,then by the proper

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) In a right-angled triangle $\Delta ABC$ where $\angle B = 90^{\circ}$,if $\overline{BM}$ is the altitude to the hypotenuse $AC$,then by the properties of similar triangles $(\Delta BMC \sim \Delta BCA)$:$\frac{BC}{AC} = \frac{MC}{BC}$Cross-multiplying gives:$BC^2 = MC \cdot AC$This implies that $BC$ is the geometric mean of $CM$ and $AC$.

Class 10 Mathematics Triangles Criteria for Similarity of Triangles

Medium

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. Then,$BC$ is the geometric mean of..........

A
$BM$ and $AC$
B
$AM$ and $CM$
C
$CM$ and $AC$
D
$AM$ and $AC$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Triangles

Subtopic

Criteria for Similarity of Triangles

In the figure,$\angle ACB = 90^{\circ}$ and $CD \perp AB$. Prove that $\frac{BC^{2}}{AC^{2}} = \frac{BD}{AD}$.

Medium

View Solution

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 $DM^{2} = DN \cdot MC.$

Difficult

View Solution

Diagonals of a trapezium $PQRS$ intersect each other at the point $O$. Given $PQ \parallel RS$ and $PQ = 3 RS$. Find the ratio of the areas of triangles $POQ$ and $ROS$.

Medium

View Solution

If $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow XZY$,and the perimeter of $\Delta ABC$ is $45$,the perimeter of $\Delta XYZ$ is $30$,and $AB = 21$,find the length of $XZ$.

Medium

View Solution

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.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. Then,$BC$ is the geometric mean of..........

Similar Questions

In the figure,$\angle ACB = 90^{\circ}$ and $CD \perp AB$. Prove that $\frac{BC^{2}}{AC^{2}} = \frac{BD}{AD}$.

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 $DM^{2} = DN \cdot MC.$

Diagonals of a trapezium $PQRS$ intersect each other at the point $O$. Given $PQ \parallel RS$ and $PQ = 3 RS$. Find the ratio of the areas of triangles $POQ$ and $ROS$.

If $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow XZY$,and the perimeter of $\Delta ABC$ is $45$,the perimeter of $\Delta XYZ$ is $30$,and $AB = 21$,find the length of $XZ$.

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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module