Math, asked by prernasingh8798, 1 month ago

In ∆ABC,D is the midpoint of side AC such that BD= 1/2AC.Show that angle ABC is a right angle?

Answers

Answered by Kaushalsingh74883508
2

Step-by-step explanation:

D is mid-point of AC

AD=DC=

2

1

AC

But BD=

2

1

AC (given)

AD=DC=BD

In ΔABD

AD=BD

∠2=∠1=x (angles opposite to equal sides are equal)

Also BD=DC

∠3=∠4=x

In ΔABC

∠1+(∠2+∠3)+∠4=180

0

x+(x+x)+x=180

0

4x=180

0

x=45

0

∠ABC=x+x=45

0

+45

0

=90

0

Hence proved.

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