ABC is a triangle in which AB = AC and D is any point on BC. Prove that :

AB² - AD² = BD.CD

ABC is an isosceles triangle with AB = AC = 2a and BC = a. If AD ⊥ BC, find the length of AD.

The perimeter of a parallelogram ABCD = 40 cm, AB = 3x cm, BC = 2x cm and CD = 2(y + 1) cm. Find the values of x and y.

ABCDE is a pentagon in which AB = AE, BC = ED and ∠ABC = ∠AED.

(a) Prove that :

(i) AC = AD

(ii) ∠BCD = ∠EDC

(b) If BC and ED are produced to meet at X, prove that BX = EX.