Question

which congruency theorem can be used to prove that \\( \triangle abd \cong \triangle dca \\)?
sss
asa
sas
aas

Explanation:

Step1: Identify equal sides

From the figure, \(AB = DC\) (marked with one tick).

Step2: Identify common side

\(AD\) is common to both \(\triangle ABD\) and \(\triangle DCA\), so \(AD=AD\).

Step3: Identify equal angles

\(\angle BAD=\angle CDA = 90^{\circ}\).

Step4: Apply congruence theorem

Since we have two sides and the included angle equal (\(AB = DC\), \(\angle BAD=\angle CDA\), \(AD = AD\)), by the SAS (Side - Angle - Side) congruence theorem, \(\triangle ABD\cong\triangle DCA\).

Answer:

C. SAS