Question

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

Answer 1

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

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.