With BC as the edge, make an equilateral triangle BCE to connect AE in triangle ABC.

AB = AC, angle DAC = 20.

Angle ABC= Angle ACB=80 degrees.

Triangle BCE is an equilateral triangle.

Angle DAC= angle ACE = 20.

Is AB=AC, AE=AE, BE=CE.

A triangle is an congruent triangle.

Angle BAE= Angle CAE = 10.

Factor angle ACD = 10.

So angle ACD= angle CAE = 10.

Because angle DAC= angle ACE=20, AC=CA.

So the triangle ADC congruent triangles CAE.

So AD=EC

Because EC=CB in equilateral triangle BCE

So AD=CB

Properties of triangles

1. On the plane, the sum of the interior angles of a triangle is equal to 180 (interior angle sum theorem).

2. On the plane, the sum of the outer angles of a triangle is equal to 360 (the theorem of the sum of outer angles).

3. On the plane, the outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

4. There are at least two acute angles among the three internal angles of a triangle.

5. At least one angle in the triangle is greater than or equal to 60 degrees, and at least one angle is less than or equal to 60 degrees.

6. The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.