Triangle Proofs

Question

Given:CA bisects ∠BAD

AC⊥BD

Prove:  △BAE≅△DAE

Answer 1

You could prove triangle BAC congruent to triangle DAC by SAS

CA bisects <BAD, AC perpendicular to BD Given

m<BAC = m<DAC Definition of angle bisector

<BCA = <DCA right angles Two perpendicular lines form right angles

m<BCA = m<DCA = 90 Right angles are 90 degrees

AC = AC Reflexive Property

BAC congruent to DAC SAS

Answer 2

△BAC and △DAC are right triangles.

m∠BAC = m∠BAC ← given that AC bisect ∠BAD

m∠BCA = m∠DCA = 90° ← given that AC⊥BD

m∠B = m∠D → complementary angles in their respective triangles

BA = DA → △ BAD is isosceles triangle

AC is common.

BC = CD → Pythagorean theorem

△BAC ≅ △DAC → SSS

P.S.

There is the capital letter "E" in names of triangles to prove congruence.

I assumed it was a typo. It's not mentioned anywhere else.