Question

In the given figure, seg AD = seg EC and AD || EC then

• A. ∆ ADB ≅ ∆ EBC by SAS test
• B. ∆ ADB ≅ ∆ EBC by SAS test
• C. ∆ ABD ≅ ∆ EBC by AAS test
• D. ∆ ABD ≅ ∆ BEC by SSS test

Answer 1

The correct option is C ∆ ABD ≅ ∆ EBC by AAS test

In the given figure, seg AD = seg EC,
Consider ∆ ABD and ∆ EBC,
∠ ADB = ∠ CEB (Alternate angles since AB ||EC )
∠ ABD = ∠ CBE (Vertically opposite angles)
& seg AD = seg EC (given)
Therefore, ∆ ABD ≅ ∆ EBC (AAS test).