Question

Prove that the four triangles formed by joining the midpoints of the sides of a parallelogram are congruent to each other.​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step 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=  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