Question

let ABC be a triangle (angle A on the top , angle B on the left , angle C on the right ) . a line AD bisects angle A and meet on the side BC , and AB = DC , prove that angle A is 72 degree ?

Answer 1

in triangle adc and triangle abc . we have to prove them. we need 3 criteria to prove .
1. AB = DC ( GIVEN )
2. ANGLE ADB = ANGLE ADC ( EACH 90 DEGREE)
3. ANGLE BAD = ANGLE CAD ( BISECTOR OF ANGLE A)
THUS , TRIANGLE adc is congruent to triangle abc by asa property.
ANGLE a is proved by cpct