In a quadrilateral ABCD, a line segment BD is a diagonal such that \(AB = CD\) and \(\angle ABD = \angle CDB\). Are the triangles ABD and CDB congruent? If so, by what rule?
Yes, by SAS
Step 1 – list the corresponding parts of ΔABD and ΔCDB:
1. \(AB = CD\) (given) — one pair of sides.
2. \(\angle ABD = \angle CDB\) (given) — angle between the equal side AB / CD and the common side BD.
3. \(BD = DB\) (common) — second pair of sides.
Step 2 – identify the rule:
Two sides and the included angle of one triangle are equal to two sides and the included angle of the other. This is the SAS (Side-Angle-Side) congruence rule.
Hence \(\triangle ABD \cong \triangle CDB\) by SAS.
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