Question

In the figure, Triangle BAT is congruent Triangle CAT. Which statement is true by CPCTC?

Answer 1

Answer: $\overline{BA}\cong\overline{CA}$

Step-by-step explanation:

Given : $\triangle {BAT}\cong\triangle{CAT}$

The CPCTC property of congruent triangles says that the corresponding parts of congruent triangles are congruent.

Therefore, the the corresponding angles and sides of $\triangle {BAT}\text{ and }\triangle{CAT}$ are congruent.

i.e. $\angle {BAT}\cong\angle{CAT}$

$\angle {ATB\cong\angle{ATC}$

$\angle {TBA}\cong\angle{TCA}$

and

$\overline{BA}\cong\overline{CA}\\\\\overline{AT}\cong\overline{AT}\\\\\overline{TB}\cong\overline{TC}$

So, from all the options $\overline{BA}\cong\overline{CA}$ is the true option.

Answer 2

CPCTC = corresponding parts of congruent triangles are congruent

BA and CA are corresponding sides for both triangles, namely twins, BA ≅ CA.