Question

complete the proof
given: \\( \overline { b c } \cong \overline { d a }, \angle c b d \cong \angle a d b \\)
prove: \\( \triangle b c d \cong \triangle d a b \\)
complete the proof below.

statement	reasons

Explanation:

Step 1: Identify the given information

We are given that \( \overline{BC}\cong\overline{DA}\) and \( \angle CBD\cong\angle ADB\). Also, note that \( \overline{BD}\cong\overline{DB}\) (common side).

Step 2: Apply the Side - Angle - Side (SAS) congruence criterion

In \( \triangle BCD\) and \( \triangle DAB\):

• \( \overline{BC}\cong\overline{DA}\) (given)
• \( \angle CBD\cong\angle ADB\) (given)
• \( \overline{BD}\cong\overline{DB}\) (reflexive property of congruence)

By the SAS (Side - Angle - Side) congruence criterion, \( \triangle BCD\cong\triangle DAB\).

For the first row in the proof table, the reason for \( \overline{BC}\cong\overline{DA}\) is "Given".

Answer:

1. Given