Question

If X,Y,Z are respectively the mid points of sides PQ, QR and PR of an equilateral
angle PQR, prove that angle XYZ is also an equilateral triangle.​

Answer 1

Answer:

Given: x,y and z are the mid-point of the sides PQ,QR and RP of ΔPQR,xy and xz are joined.

Prove: XYRZ is a parallelogram.

In PQR,x,y, and z are the mid-point of PQQR and RP respectively.

XY∣∣PR (mid-point theorem)

XY=

2

1

PR (mid-point theorem)

ZR=

2

1

PR (Given)

Therefore, XYRZ is a Parallelogram (One pair of opposite sides parallel and equal)

Hence proved.