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Question

ABC and DBC are two isosceles triangle on the same side of BC. Then, DA (or AD) produced bisects BC at right angle.
If the above statement is true then mention answer as 1, else mention 0 if false

Solution
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Join AD.Let it meet BC in O
In ABO and ACO,
AB = AC (Given)
ABO=ACO (ABD is an isosceles tiangle)
AO = AO (Common side)
ABOACO (By SSA congruence rule)
Hence, AOB=AOC=x (Corresponding angles of congruent triangles)
Now, AOB+AOC=180
x+x=180
x=90
Thus, AD bisects BC at right angles.
195400_177256_ans_c5178fe28a104aa8811bd97d6466c886.png

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