If the bisector of an angle of a triangle also bisect the opposite
side. Prove that the triangle is isosceles.
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Given, △ABC, AD bisects ∠A and AD bisects BC.
To prove: ABC is an Isosceles triangle
In △ABD and △ACD
∠DAB=∠DAC (AD bisects ∠A)
AD=AD (Common)
BD=CD (AD bisects BC)
Thus, △ABD≅△ACD (SAS rule)
Thus, AB=AC (By cpct)
hence, ABC is an Isosceles triangle.
To prove: ABC is an Isosceles triangle
In △ABD and △ACD
∠DAB=∠DAC (AD bisects ∠A)
AD=AD (Common)
BD=CD (AD bisects BC)
Thus, △ABD≅△ACD (SAS rule)
Thus, AB=AC (By cpct)
hence, ABC is an Isosceles triangle.
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