In triangle ABC, the sides AB and AC are equal. If P is a point on AB and Q is a point on AC such that AP = AQ, prove that :
(i) triangle APC and AQB are congruent.
(ii) triangle BPC and CQB are congruent.

In triangle ABC, D is a point in side AB such that AB = 4AD and E is a point in AC such that AC = 4AE. Show that BC : DE = 4:1

The following figure shows a triangle ABC in which AB=AC. M is a point on AB and N is a point on AC such that BM = CN. Prove that BN=CM

The following figure shows a triangle ABC in which AB=AC. M is a point on AB and N is a point on AC such that BM = CN. Prove that AM=AN

The following figure shows a triangle ABC in which AB=AC. M is a point on AB and N is a point on AC such that BM = CN. Prove that DeltaAMC~=DeltaANB

ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that the triangles ADX and BAY are congruent.

ABC is a triangle in which AB = AC and D is a point on AC such that BC^2 = AC xx CD .Prove that BD = BC .

The following figure shows a triangle ABC in which AB=AC. M is a point on AB and N is a point on AC such that BM = CN. Prove that DeltaBMC~=DeltaCNB

In the given figure, AB||CD and AB=CD , prove that: triangle AOB is congruent to triangle DOC.

In the parallelogram ABCD ,M is mid-point of AC and X,Y are points on AB and DC respectively such that AX = CY. Prove that : (i) Triangle AXM is congruent to triangle (ii) XMY is a straight line.

The following figure shows a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN. Prove that : (i) AM = AN (ii) Delta AMC ~= Delta ANB (iii) BN = CM (iv) Delta BMC ~= Delta CNB