In triangle ABC, with sides CA congruent to CB and altitude CD perpendicular to AB, the correct triangle congruence theorem is C. HL (Hypotenuse-Leg).
The question pertains to triangle congruence theorems which are used to determine if two triangles are congruent.
In the given scenario, triangle ABC has CA congruent to CB, and CD is perpendicular to AB.
This indicates that triangle ABC is isosceles with CA and CB as the congruent sides, and CD being the altitude, it bisects the base AB.
Therefore, triangles ACD and BCD are right triangles that share a hypotenuse and have a congruent leg making them congruent by the HL (Hypotenuse-Leg) theorem.
The correct answer is C. HL because no information about angles or the other sides is provided, ruling out A. SSS, B. SAS, and D. AAS.
The probable question may be:
In triangle ABC Given that CA congurent CB and CD is perpendicular to AB.
The answer choices are:
SSS
SAS
HL
AAS