Points B and D are marked on different sides of the straight line AC, so that the angle BAC = angle CAD

univerkov | March 1, 2021 | education

Points B and D are marked on different sides of the straight line AC, so that the angle BAC = angle CAD, angle BCA = angle DСА. AB = 5cm, BC = 8cm. What is the length of the CD?

Consider triangles ABC and ADC.

By condition, the angle BAC = CAD, and the angle BCA = DCA.

The AC side of both triangles is common.

Then triangles ABC and ADC are equal in the second sign of equality of triangles – in two angles and a side.

Equal triangles have equal sides opposite equal angles, then side CD = BC = 8 cm.

Answer: СD = 8 cm.

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