## Elementary Geometry for College Students (6th Edition)

1- in a triangle ABC, $\angle A + \angle B = 90^{\circ}$ since its a right triangle. 2-in a triangle ADC, $\angle A + \angle ACD = 90^{\circ}$ same reason as step one. 3- by angle addition property, $\angle A + \angle B= \angle A + \angle ACD$ therefore $\angle B= \angle ACD$. 4- $\angle B + \angle BCD = 90^{\circ}$ and $\angle A + \angle ACD = 90 ^{\circ}$ 5- by substitution, and since $\angle ACD = \angle B$ in step three, therefore $\angle A= \angle BCD$ 6- triangle ACD ~ triangle CBD by AA. 7- $\angle B = \angle B$ and $\angle A = \angle A$ identity. 8- $\angle ADC = \angle BDC = ACB$ right angles are congruent. 9- triangle ACD ~ triangle CBD ~ triangle ABC $\square$