Can the theorem of isosceles triangle be proved by doing a different c – InterviewSolution

InterviewSolution

1.

Can the theorem of isosceles triangle be proved by doing a different construction?

Answer»

Yes

Construction:

Draw seg AD ⊥ seg BC.

Proof:

In ∆ABD and ∆ACD,

seg AB≅ seg AC [Given]

∠ADB ≅ ∠ADC [Each angle is of measure 90°]

seg AD ≅ seg AD [Common side]

∴ ∆ABD ≅ ∆ACD [Hypotenuse side test]

∴ ∠ABD ≅ ∠ACD [c.a.c.t.]

∴ ∠ABC ≅ ∠ACB [B - D - C]

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