Prove that the triangles formed by joining in pairs, the mid points of the three sides of a triangle are congruent to each other.

Asked by Topperlearning User | 11th Aug, 2017, 11:59: AM

Expert Answer:

ABC is a triangle in which D, E and F are the mid points of the sides BC, CA and AB respectively.
F and E are the mid points of AB and AC respectively
FE  BC and FE = size 12px 1 over size 12px 2BC                (By mid point theorem)
FE = BD
In AFE and FBD,
AF = FB
FE = BD
AFE = FBD                                 (corresponding angles)
AFE  FBD                            (SAS)
Similarly you can prove that the other pairs of triangles are also congruent.

Answered by  | 11th Aug, 2017, 01:59: PM