Question

prove that the four triangles formed by joining the mid point of the three sides of a triangle are congruent to each other

Answer 1

first, draw a triangle ABC,
let P, Q,R be the midpoints of sides AB, AC, BC respectively..

we know that,
PQ=1/2 BC -(1)
PR=1/2AC -(2)
QR=1/2AB -(3)
..by mid point theorem
Given that:
AP=BP= 1/2AB =QR (from 3)
AQ=QC=1/2AC =PR (from 2)
BR=RC=1/2BC = PQ (from 1)

now considering 3 pairs of triangles, we can prove that all 4 triangles are equal by SSS congruence rule.
hope u understood!

Answer 2

Step-by-step explanation:

Hope u like it..

thank you ....