# Inside the undeveloped angle A, point D is taken, from which the perpendiculars DB and DC

May 29, 2021 | education

| **Inside the undeveloped angle A, point D is taken, from which the perpendiculars DB and DC are drawn to the sides of the angle. Angle ADB = angle ADC. Prove that the ray AD is the bisector of angle A.**

Since, by condition, DB and DC are perpendiculars to AB AC, the triangles ABD and ACD are rectangular.

In right-angled triangles ABD and ACD, the angle ADB = ADC by condition, and the hypotenuse AD is common in construction, then right-angled triangles ABD and ACD are equal in the third sign of equality of right-angled triangles, in hypotenuse and acute angle, which means the angle BAD = angle CAD, and therefore , AD is the bisector of the angle BAC, as required.

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