In a right-angled triangle ABC with D as the midpoint of side AB, angle ACD is proven congruent to angle BAC using the ASA congruence criterion, given the right angle at D and the reflexive property of side CA.
In the given right-angled triangle ABC, with angle DAB as a right angle (given), and D being the midpoint of side AB, we observe that side CA is congruent to itself, following the Reflexive Property. To establish the congruence between angle ACD and angle BAC, we can apply the Angle-Side-Angle (ASA) congruence criterion.
Considering triangle ACD and triangle BAC, we have:
- Angle ACD (angle adjacent to side CA)
- Side CA (common side)
- Angle BAC (angle opposite to side CA)
By the ASA congruence criterion, the two triangles are congruent. Therefore, angle ACD is congruent to angle BAC in the right-angled triangle ABC with D as the midpoint of side AB.