Question

In the figure in ΔABC, AD is ⊥ BC and BD = DC.

∴ ΔABD ≅ ΔACD by ______.

Options

• RHS

• AAS

• SAS

• SSA

Answer 1

∴ ΔABD ≅ ΔACD by SAS.

Explanation:

To prove ΔABD ≅ ΔACD, we consider:

1. BD = DC  ...(Given)
2. AD = AD  ...(Common side)
3. ∠ADB = ∠ADC = 90°  ...(Since AD is ⊥ to BC)

These satisfy the SAS (Side-Angle-Side) congruence condition two sides and the included angle are equal in both triangles. 

Hence, ΔABD ≅ ΔACD by SAS.