Math, asked by rammurti3636, 9 months ago

Let ABC be an isosceles triangle in which AB=AC. If D, E, F be the mid-points of the sides BC, CA and AB respectively, show that the segment AD and EF bisect each other at right angles.

Answers

Answered by presentmoment
4

The segment AD and EF bisect each other at right angles.

Step-by-step explanation:

Given data:

ΔABC is an isosceles triangle.

AB = AC

D, E, F are midpoint of sides BC, CA and AB respectively.

Let AD and EF intersect at O.

In ΔABD and ΔACD,

AB = AC (S)

∠ADB = ∠ADC = 90° (A)

∠BAD = ∠CAD (A)

By ASA congruence rule, ΔABD ≅ ΔACD.

In ΔEAO and ΔFAO,

∠EAO = ∠FAO (A)

AE = AF (S)

AO = AO (S)

By SAS congruence rule, ΔEAO ≅ ΔFAO.

By CPCT,

∠EOA = ∠FOA = 90°

EO = FO

Hence proved.

To learn more...

1. ABC is an isoceles triangle with AB=AC.D,E and F are mid points of the sides BC,AB and AC respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.

https://brainly.in/question/6621172

2. ABC is an isosceles triangle with AB = AC and let D, F, E be the mid-points of BC, CA and AB respectively. Show that AD is perpendicular to EF and AD bisects EF.

https://brainly.in/question/6233364

Answered by MissUnknownHere
2

Answer:

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