Question

In A ABC, AD is the perpendicular bisector of BC (see figure). Show that AABC is an
isosceles triangle in which AB = AC.​

Answer 1

QUESTION :-

In ∆ ABC, AD is the perpendicular bisector of BC (see figure). Show that ∆ ABC is an isosceles triangle in which AB = AC.

SOLUTION :-

Given :-

AD is the perpendicular bisector of BC.

To prove :-

In ∆ABC is an isosceles triangle. i.e., AB = AC

Prove :- In ∆ ADB and ∆ ADC,

AD = AD [common]

BD = DC (Given)

and ∠ADB = ∠ADC [each= 90°]

∆ ADB ≅ ∆ ADC (By SAS congruence axiom)

AB = AC (By CPCT)

So, ∆ ABC is an isosceles triangle.

Answer 2

Answer:

Solution:

Since AD is bisector of BC.

∴ BD = CD

Now, in ∆ABD and ∆ACD, we have

AD = DA [Common]

∠ADB = ∠ADC [Each 90°]

BD = CD [Proved above]

∴ ∆ABD ≅ ∆ACD [By SAS congruency]

⇒ AB = AC [By C.P.C.T.]

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Thus, ∆ABC is an isosceles triangle

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