Triangle ABC is isosceles (BC = AC). Point D is taken inside the triangle so that BD = AD

| August 7, 2021 | education

Triangle ABC is isosceles (BC = AC). Point D is taken inside the triangle so that BD = AD, angle ADB = 120 ‘, angle A = 60’. Find BDC Angle and DAC Angle

1) Consider triangles CDB and CDA:

AC = BC (by condition), DА = DB (by condition), CD – common side for both triangles. This means that the triangles CDB and CDA are equal on the third basis (on three sides).

Therefore, the CDB angle is equal to the CDA angle.

Angle CDB + angle CDA + angle ADB = 360 °, which means angle BDC = CDA = (360 ° – 120 °): 2 = 140 °: 2 = 120 °.

2) Consider a triangle ADB: DA = DB (by condition), which means that triangle ADB is isosceles, and therefore the angle DAB = angle DBA (the angles at the base of an isosceles triangle are equal).

The sum of the angles in the triangle is 180 °: DAB = DBA = (180 ° – 120 °): 2 = 60 °: 2 = 30 °.

Hence it follows that the angle DAC = 60 ° – 30 ° = 30 °.

Answer: angle ВDC = 120 °, angle DAC = 30 °.



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