ABCDE is a pentagon in which AB = AE, BC = ED and ` angle ABC = angle AED. `
Prove that
AC= AD
(ii) ` angle BCD= angle EDC`

In the following figure AB = AD , AC = AE and angle BAD = angle CAE, Prove that :BC = ED

In a quadrilateral ABCD, AB = CD and angle B = angle C . Prove that AC = AB

In the given figure, AC = AE, AB = AD and angle BAD = angle EAC . Show that : BC = DE.

In a quadrilateral ABCD, AB = CD and angle B = angle C . Prove that AD is parallel to BC.

Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency : (a) In Delta ABC and Delta DEF , AB = DE, BC = EF and angle B = angle E . (b) In Delta ABC and Delta DEF, angle B = angle E = 90^(@) , AC = DF and BC = EF. (c) In Delta ABC and Delta QRP , AB = QR, angle B = angle R and angle C = angle P . (d) In Delta ABC and Delta PQR , AB = PQ, AC = PR and BC = QR. (e) In Delta ABC and Delta PQR , BC = QR, angle A = 90^(@), angle C = angle R = 40^(@) and angle Q = 50^(@) .

In the following diagram, AD = AB and AE bisects angle A. Prove that : (i) BE = DE (ii) angleABD gt angleC

ABC is a right triangle with AB = AC .If bisector of angle A meet BC at D then prove that BC = 2 AD .

In parallelogram ABCD, E is the mid-point of side AB and CE bisect angle BCD. Prove that : (i) AE=AD (ii) DE bisect angleADC and (iii) Angle DEC is a right angle.

In quadrilateral ABCD, AD = BC and BD = CA. Prove that : (i) angle ADB = angle BCA (ii) angle DAB = angle CBA

In a quadrilateral ABCD, AB= AD and CB= CD. Prove that: AC bisects angle BAD