Question

1. in the figure, △abd≅△cbd by angle - side angle (asa). which segments are congruent by cpctc?

Explanation:

Step1: Recall CPCTC concept

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. If $\triangle ABD\cong\triangle CBD$ by ASA, we match the corresponding vertices. A corresponds to C, B is common, and D is common.

Step2: Identify corresponding segments

The corresponding segments are: $\overline{AB}$ and $\overline{CB}$, $\overline{AD}$ and $\overline{CD}$, $\overline{BD}$ and $\overline{BD}$ (the common - side).

Answer:

$\overline{AD}\cong\overline{CD}$, $\overline{AB}\cong\overline{CB}$

Since the options provided in the image are not fully clear in text (the last two options seem to be cut - off), but based on the principle of CPCTC for $\triangle ABD\cong\triangle CBD$ by ASA, the correct congruent segments are $\overline{AD}\cong\overline{CD}$ and $\overline{AB}\cong\overline{CB}$. If we assume the third option is $\overline{AB}\cong\overline{CB}$, that would be the correct choice among the given ones.