If the bisector of the vertical angle bisects the base of the triangle. Prove that the triangle is isosceles triangle.
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If the bisector of the vertical angle bisects the base of the triangle. Prove that the triangle is isosceles triangle.
Answer this question, I will mark your answer as brainlist.
No spam otherwise I will report your answer.
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Step-by-step explanation:
Construction
Produce AD to E such that AD=DE Join EC
Proof : In △ADB and △EDC
BD=CD ( given)
AD=ED ( by construction)
∠ADB=∠EDC ( vertically opposite angles)
∴△ADB≅△EDC ( SAS congruence)
∴AB=ED−−−−−(1) ( by CPCT)
and ∠BAD=∠CED ( by CPCT)
But ∠BAD=∠CAD (given)
∴∠CAD=∠CED
∴AC=CE−−−−−−−(2) ( sides opposite to equal angles of a triangle are equal.
From (1) and (2), AB=AC
∴△ABC is isosceles.
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