Question

In ABC and DBC are two isosceles triangle drawn on opposite sides of the sam ABC and DBC are two isosceles triangle drawn on the opposite side of the same base BC and AE joined prove that ad bisects each of the angle angle BAC and B DC e base bc and a, d are joined, prove that and bisects each of the angle back and bdc

Answer 1

Answer:

Step-by-step explanation:

construction:- draw AE and DE perpendicular to BC

now, in triangle triangle AEC and triangle AEB

AE = AE ( common)

CE = BE ( as perpendicular bisects base in an isosceles triangle)

angle AEC = angle AEB ( each 90)

therefore, triangle AEC is congruent to triangle AEB( by RHS congruency rule)

so, angle EAB = EAC ( corresponding parts of congruent triangles)

similarly, triangle BDE = triangle CDE

therefore angle BDE = angle CDE