Question

Prove that the four triangle formed by joining in pairs the mid-point of the sides of a tringle are congruent to each other​

Answer 1

Answer:

Explanation:

Given :

A triangle of ABC and D,E,F are  the mid-points of sides BC,CA and AB respectively.

To prove :

△AFE≅△FBD≅△EDC≅△DEF.

Proof :

Since the segment joining the mid-points of the sides of a triangle is half of the third side. Therefore,

DE=  

2

1

​  

AB⟹DE=AF=BF          ..........(1)

EF=  

2

1

​  

BC⟹EF=BD=CD           .........(2)

DF=  

2

1

​  

AC⟹DF=AE=EC           ..........(3)

Now, in △s DEF and AFE,  

DE=AF

DF=AE

and, EF=FE

So, by SSS criterion of congruence,

△DEF≅△AFE

Similarly, △DEF≅△FBD and △DEF≅△EDC

Hence, △AFE≅△FBD≅△EDC≅△DEF

Answer 2

Given :

A triangle of ABC and D,E,F are the mid-points of sides BC,CA and AB respectively.

To prove :

△AFE ≅ △FBD ≅ △EDC ≅ △DEF

Proof :

Since the segment joining the mid-points of the sides of a triangle is half of the third side. Therefore,

DE = 1/2 AB

DE = AF = BF ••••••••••••••••••••• (1)

EF = 1/2 BC

EF = BD = CD ••••••••••••••••••••• (2)

DF = 1/2 AC

DF = AE = EC ••••••••••••••••••••• (3)

Now, in △s DEF and AFE,

DE=AF

DF=AE

and, EF=FE

So, by SSS criterion of congruence,

△DEF≅△AFE

Similarly, △DEF≅△FBD and △DEF≅△EDC

Hence, △AFE≅△FBD≅△EDC≅△DEF

Hope this helps you ☺️

Please mark as brainliest if your satisfied with my answer......