In a right triangle ABC, angle C is a right angle and CD is perpendicular to AB . Prove triange BCA similar to triangle CDA

Answer 1

Angle CAB = angle DAC is shared (reflexive property

angle ABC = angle ACD = 90 are congruent right angles

By congruent angle theorem,

angles CAB + CBA = 90 = DAC + DCA

So, CBA = DAC after subtracting CAB=DAC from both sides

Therefore, corresponding angles are congruent, which proves the triangles are similar