If M is the mid – point of the hypotenuse AC of right ΔABC then BM=

If M is the mid - point of the hypotenuse AC of right $Δ A B C$ then $B M =$

A
AC
B
2AC
C
$\frac{1}{2}$ AC
D
$\frac{1}{3}$ AC

Solution:

Given in $Δ A B C, ∠ B = 90 °$ and $A M = M C$ Produce BM to D such that $B M = M D$

$Δ A B M Δ D C M$

$A M = M C$

$∠ A M B = ∠ C M D (V . O . A . E)$

$B M = M D$

$∴$ By S.A.S congruence $Δ A B M ≅ Δ C D M$

$A B = C D$

$∠ B A M = ∠ M C D$

$A B | | D C$

$∠ D C B = 90 °$

$∴ Δ A B C ≅ Δ D C B$

$\Rightarrow A C = B D$

$\Rightarrow A C = 2 B M$

$\Rightarrow B M = \frac{1}{2} A C$

Related content

Pad Parichay Class 10 MCQ CBSE

BITSAT Sample Papers 2025 (Available) – Online Paper PDF Download

Is or Are Worksheet

Parts of Speech Worksheets with Answers

GK Questions on Guru Nanak Jayanti 2024

GK Questions on Guru Nanak Dev Ji

Ray Optics and Optical Instruments MCQs for NEET Physics

World Pneumonia Day

How Many Days Left for NEET 2025?

Children’s Day Board Decoration Ideas for Students