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SAS Postulate

Question 2In ...

Question

Question 2
In $Δ A B C, A D$ is the perpendicular bisector of BC (see the given figure).
Show that $Δ A B C$ is an isosceles triangle in which AB = AC.

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Solution

$I n Δ A D C a n d Δ A D B, A D = A D (C o m m o n) ∠ A D C = ∠ A D B (E a c h 90^{\circ}) C D = B D (A D i s t h e p e r p e n d i c u l a r b i s e c t o r o f B C) ∴ Δ A D C ≅ Δ A D B (B y S A S c o n g r u e n c e r u l e) ∴ A B = A C (B y C P C T) T h e r e f o r e, A B C i s a n i s o s c e l e s t r i a n g l e i n w h i c h A B = A C$

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