Question

1. in the figure, δbat ≅ δcat. which statement is not true by cpctc?

ta = at
∠bca = ∠bct
tb = tc
∠abt = ∠act

Explanation:

Step1: Recall CPCTC concept

CPCTC (Corresponding - Parts of Congruent Triangles are Congruent) means that if two triangles are congruent, their corresponding sides and corresponding angles are congruent. Given $\triangle BAT\cong\triangle CAT$.

Step2: Analyze each option

• Option 1: $\overline{TA}\cong\overline{AT}$ is a reflexive property and is always true for the same segment.
• Option 2: $\angle BCA$ and $\angle BCT$ are not corresponding angles of $\triangle BAT$ and $\triangle CAT$. They are not related by the congruence of $\triangle BAT$ and $\triangle CAT$.
• Option 3: $\overline{TB}\cong\overline{TC}$ because they are corresponding sides of congruent triangles $\triangle BAT$ and $\triangle CAT$.
• Option 4: $\angle ABT\cong\angle ACT$ because they are corresponding angles of congruent triangles $\triangle BAT$ and $\triangle CAT$.

Answer:

$\angle BCA\cong\angle BCT$