Point B is taken on the bisector of angle A, and points C and D on the sides of the angle

| September 8, 2021 | education

Point B is taken on the bisector of angle A, and points C and D on the sides of the angle, such that the triangular ABC = ABD. prove that AD = AC.

Consider triangles: ABC and ABD, according to the problem statement, they are equal, that is, the corresponding sides are equal, which are opposite to equal angles. Consider these equal sides, and equal angles.

1) Side AB is common (it’s like equal sides), which means that the angles are <BCA = <BDA;

2) Angles <CAB = <DAB, as angles separated by the bisector AB, angle <A, hence the sides BC = BD, as sides against equal angles.

3) Consider the angles <CBA = (180 – <BCA – <CAB) and <DBA = (180 – <BDA – <DAB), they are equal, since equal angles are subtracted. This means that the sides are equal: AC = AD.



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