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Angle DAB = angle DAC as AD is the bisector of angle A.

angle ADB = exterior angle to triangle ADC at D. = angle DAC + angle C angle ADC = exterior angle to triangle ADB at D = angle DAB + angle B = angle DAC + angle B if angle C is greater, then angle ADB is greater. ======================== 2. angle ABD + angle DBC = 90 angle ABD = 90 - angle DBC = 90 - (90 - angle C), = angle C as in right angle triangle DBC, angle BDC = 90, so angle DBC = 90 - angle C. ============ similar to the above proof.

in right angle triangle ABD, angle D = 90. so angle ABD + angle A = 90 so angle ABD = 90 - angle A.

Now angle CBD = 90 - angle ABD = 90 - (90 - angle A) = angle A.