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
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
Answer:
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