Answer:
The correct answer to this problem is the final option, angle BTA is congruent to angle ATC.
Step-by-step explanation:
To solve this problem, we first have to unpack the meaning of the given information. First, let's remember that CPCTC means that corresponding parts of congruent triangles are congruent. This means that the same parts of two different triangles that are stated to be congruent (the same) are thus also congruent (the same).
In this case, triangle BAT and triangle CAT are stated to be congruent. This means that line segment BA and CA are congruent, angles BAT and CAT are congruent, and more because of CPCTC (explained above).
The correct answer to this problem is the final option, angle BTA is congruent to angle ATC. We can figure this out simply by looking at the triangle names. Angle ATC is the same as angle CTA (the letters are just in reverse order). From the congruence statement, we can tell that BTA and CTA are congruent angles due to the fact that triangle BAT and CAT are congruent using CPCTC. Looking at the figure, this makes sense because these two angles appear to be the same measure.
Also, we can eliminate the other answer choices, since they are not corresponding parts of the two triangles (the line segments and angles do not represent two congruent pieces of the triangle - they are not matched up correctly).
Hope this helps!
