Question

14 given: $overline{ad}congoverline{cd}$, $angle adbcongangle cdb$ prove: $\triangle adbcong\triangle cdb$ $overline{ad}congoverline{cd}$ and $angle adbcongangle cdb$ (given). $overline{bd}congoverline{bd}$ by the _________ of $cong$, so $\triangle adbcong\triangle cdb$ by _________.

Explanation:

Step1: Identify common side

The line segment BD is common to both \(\triangle ADB\) and \(\triangle CDB\), so \(\overline{BD}\cong\overline{BD}\) by the reflexive property of congruence.

Step2: Apply congruence criterion

We are given \(\overline{AD}\cong\overline{CD}\) and \(\angle ADB\cong\angle CDB\), and we have \(\overline{BD}\cong\overline{BD}\). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle ADB\cong\triangle CDB\).

Answer:

Reflexive property; SAS