Log in to add a comment

## Answers

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

**⇒ In Right angled triangle ABC ,**

__GIVEN ;-__

**⇒ In the below figure , it is given that D is midpoint of AC.**

**⇒ We need to prove that , - BD = 1 / 2 × AC**

TO PROVE :-

TO PROVE :-

**⇒In Δ ABC , The line L is parallel to AB.**

PROOF ;-

PROOF ;-

**⇒Therefore we can say that ,**

**∠ABC = ∠DEC = 90° { As line L is parallel to AB}**

__Δ ABC,__

We know that D is the mid point of AC inWe know that D is the mid point of AC in

**⇒ So - DE || AB [**

__D is the mid point of AC]__

**⇒**

**Using converse of mid point theorem we get ,**

**⇒**

**E is the mid point of DC**

⇒ Therefore BE = EC → ( Equation no . 2 )

**⇒ Now , In Δ DEB and Δ DEC,**

**⇒ ∠DEB = ∠DEC = 90º [ from Equation (1)]**

**⇒ DE = DE { Common side }**

**⇒ BE = EC [From Equation (2)]**

__So by SAS congruence rule we get__

**Δ DEB ≅ Δ DEC**

**DC = BD [ By C.P.C.T ]**

**⇒**

we know that D is the mid point of AC- so we get as ,

we know that D is the mid point of AC- so we get as ,

Therefore we get as BD = 1/2 of AC

Hence proved.

Therefore we get as BD = 1/2 of AC

Hence proved.