Question

Assertion: In the figure AD ⊥ BC and BD = DC. ∴ ΔABD = ΔACD by RHS test of congruency.

Reason: Two right angled Δs are congruent if their hypotenuses are equal and one side of one Δ is equal to one side of the other.

पर्याय

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true but R is the incorrect reason for A.

Explanation:

• A is true: AD ⟂ BC, so ∠ADB = ∠ADC = 90°. Also, AD = AD (common) and BD = DC (given). Thus, the two right triangles have both legs equal, so ΔABD ≅ ΔACD (leg–leg congruence for right triangles).
• R is true as a general statement the RHS hypotenuse and one corresponding side is a valid congruence test for right triangles, but it is not the correct reason here because we do not know the hypotenuses AB and AC are equal. The triangles are congruent because both legs are equal, not because hypotenuse + one side are equal.