Assertion (A): ΔABD ≅ ΔACE

Reason (R): ∠ADE + ∠ADB = ∠AEC + ∠AED

But AD = AE

⇒ ∠ADE = ∠AED

∴ ∠ADB = ∠AEC

⇒ ∠ABD ≅ ∠AEC

1. A is true, but R is false.

2. A is false, but R is true.

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

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

Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency :

(a) In △ ABC and △ DEF, AB = DE, BC = EF and ∠B = ∠E.

(b) In △ ABC and △ DEF, ∠B = ∠E = 90°; AC = DF and BC = EF.

(c) In △ ABC and △ QRP, AB = QR, ∠B = ∠R and ∠C = ∠P.

(d) In △ ABC and △ PQR, AB = PQ, AC = PR and BC = QR.

(e) In △ ABC and △ PQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.

In the given figure : AB // FD, AC // GE and BD = CE; prove that :

(i) BG = DF

(ii) CF = EG.

In a triangle ABC, AB = AC. Show that the altitude AD is median also.