Fill in the blanks using the correct word given in brackets:

(i) All circles are __________. (congruent, similar)

(ii) All squares are ___________. (similar, congruent)

(iii) All ____________ triangles are similar. (isosceles, equilateral)

(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are _________ and (b) their corresponding sides are ___________. (equal, proportional)

It is given that ∆DEF ∼ ∆RPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P? Why?

In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.

Or

In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

In a triangle, the perpendicular from the vertex to the base bisects the base. The triangle is

In a ΔABC, it is given that AD is the internal bisector of ∠A. If AB = 10 cm, AC = 14 cm and BC = 6 cm, then CD = ?

In a ΔABC it is given that AB = 6 cm, AC = 8 cm and AD is the bisector of ∠A. Then, BD : DC = ?

D and E are points on the sides AB and AC respectively of a ΔABC. In each of the following cases, determine whether DE || BC or not.

AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC.

Find the value of x, when

AD = x cm, DB = (x - 2) cm,

AE = (x + 2) cm and EC = (x - 1) cm.

In a ΔABC, AD is the bisector of ∠A.

If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

In a ΔABC, AD is the bisector of ∠A.

If AB = 10 cm, AC = 14 cm and BC =6 cm, find BD and DC.

D and E are points on the sides AB and AC respectively of a ΔABC. In each of the following cases, determine whether DE || BC or not.

AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC =10 cm.