D, E and F are the mid-points of the sides AB, BC and CA of an isosceles △ ABC in which AB = BC. Prove that △ DEF is also isosceles.
Mid-point Theorem
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Question

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles △ ABC in which AB = BC. Prove that △ DEF is also isosceles.

KnowledgeBoat · Accepted Answer

Join D, E and F. Given, AB = BC = x (let) Given, D, E and F are mid-points of sides AB, BC and AC respectively. By mid-point theorem, The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it. ∴ DF = , FE = and DE = . In △ DEF, DF = FE. ∴ △ DEF is an isosceles triangle. Hence, proved that DEF is an isosceles triangle.

Mathematics

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles △ ABC in which AB = BC. Prove that △ DEF is also isosceles.

Mid-point Theorem

Related Questions

In triangle ABC, M is the mid-point of AB and a straight line through M and parallel to BC cuts AC at N. Find the lengths of AN and MN, if BC = 7 cm and AC = 5 cm.

Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.

The figure, given below, shows a trapezium ABCD. M and N are the mid-points of the non-parallel sides AD and BC respectively. Find :
(i) MN, if AB = 11 cm and DC = 8 cm.
(ii) AB, if DC = 20 cm and MN = 27 cm.
(iii) DC, if MN = 15 cm and AB = 23 cm.

Mathematics

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles △ ABC in which AB = BC. Prove that △ DEF is also isosceles.

Mid-point Theorem

Related Questions

In triangle ABC, M is the mid-point of AB and a straight line through M and parallel to BC cuts AC at N. Find the lengths of AN and MN, if BC = 7 cm and AC = 5 cm.

Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.

The figure, given below, shows a trapezium ABCD. M and N are the mid-points of the non-parallel sides AD and BC respectively. Find :(i) MN, if AB = 11 cm and DC = 8 cm.(ii) AB, if DC = 20 cm and MN = 27 cm.(iii) DC, if MN = 15 cm and AB = 23 cm.

The figure, given below, shows a trapezium ABCD. M and N are the mid-points of the non-parallel sides AD and BC respectively. Find :
(i) MN, if AB = 11 cm and DC = 8 cm.
(ii) AB, if DC = 20 cm and MN = 27 cm.
(iii) DC, if MN = 15 cm and AB = 23 cm.