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12/07/2021 11:37 am
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ABC and DBC are two isosceles triangles on the same base BC (see Figure). Show that ABD = ACD.
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12/07/2021 11:38 am
In the question, it is given that ABC and DBC are two isosceles triangles.
We will have to show that ABD = ACD
Proof:
Triangles ΔABD and ΔACD are similar by SSS congruency since
AD = AD (It is the common arm)
AB = AC (Since ABC is an isosceles triangle)
BD = CD (Since BCD is an isosceles triangle)
So, ΔABD ΔACD.
∴ ABD = ACD by CPCT.