Question

Show that, the triangle obtained by joining the mid points of the sides of an isosceles triangle is also an isosceles triangle. Can we get an equilateral triangle by joining the mid points of the sides of an equilateral triangle?

Answer 1

∆ ABC is an isosceles triangle. P, Q, R are the mid points of the sides of the triangle.

Consider ∆ PBR and ∆ QRC.

PB = QC

BR = CR

∠B = ∠C

Two sides and the angle made by them are equal. The third sides PR and QR also equal.

∴ ∆ PQR is an isosceles triangle. Similarly the triangle obtained by joining the mid points of the sides of an equilateral triangle is an equilateral triangle.