In a quadrilateral, AB = AD, and angle BAC = angle CAD. Prove that angles B and D are equal.

univerkov | August 19, 2021 | education

Consider triangles ABC and ACD and prove that they are equal.

By condition, AB = AD, and the angle BAC is equal to the angle CAD.

The segment AC is common for the triangles. Then triangle ABC is equal to triangle ACD according to the first sign of equality of triangles – on two sides and the angle between them.

Then in the quadrangle ABCD the angle ABC is equal to the angle ADC, which was required to be proved.

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