Question

In given below figure in triangle abc D and e are midpoints of sides bc and ac respectively find the length of DE. Prove that DE=1/2AB
A(-6,-1)
B(2,-2)
C(4,-2)

Answer 1

First Find the points D and E by midpoint formula.
(x₂+x₁/2 , y₂+y₁/2)
For DE=1/2AB
In ΔsCED and CAB
∠ECD=∠ACB
and the ratio of the side containing the angle is same i.e,
CD=1/2BC
⇒CD/BC=1/2
EC=1/2AC
⇒EC/AC=1/2
∴,ΔCED~ΔCAB
hence the ratio of their corresponding sides will be equal,
DE=1/2AB
Cheers and mark it as brainliest!!

Answer 2

Answer:

Step-by-step explanations:-

By mid point formula,

(x2 + x1 / 2 ,y2 + y1 / 2) ---{ for proving DE= 1/2 AB}

In∆ECD and ∆ ACB

<ECD = <ACB

BD =1/2 AB

BD/AB= 1/2

EC=1/2AC

EC/AC= 1/2

•°• ∆ECD~∆ACB ------ SAS CRITERION

=> DE=1/2AC.......HENCE PROVED!!