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, equilaterals).

(iv) Two triangles are similar, if heir corresponding angles are………(proportional, equal)

(v) Two triangles are similar, if their corresponding sides are………(proportional, equal)

(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles ae and (b) heir corresponding sides are………(equal, proportional)

Write the truth value (T/F) of each of the following statements:

(i) Any two similar figures are congruent.

(ii) Any two congruent figures are similar.

(iii) Two polygons are similar, if their corresponding sides are proportional.

(iv) Two polygons are similar if their corresponding angles are proportional.

(v) Two triangles are similar if their corresponding sides are proportional.

(vi) Two triangles are similar if their corresponding angles are proportional.

In a , D and E are points on the sides AB and AC respectively such that

(i) If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.

(ii) If and AC = 15 cm, find AE.

(iii) If and AC = 18 cm, find AE.

(iv) If AD = 4, AE = 8, DB = x – 4, and EC = 3x – 19, find x.

(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE.

(vi) If AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC.

(vii) If AD = 2 cm, AB = 6 cm and AC = 9 cm, find AE.

(viii) If and EC = 2.5 cm, find AE.

(ix) If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find the value of x.

(x) If AD = 8x - 7, DB = 5x – 3, AE = 4x - 3 and EC = (3x – 1), find the value of x.

(xi) If AD = 4x – 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x - 3, find the volume x.

(xii) If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.

In a, D and E are points on the sides AB and AC respectively. For each of the following cases show that :

(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.

(ii) AB = 5.6 cm, AD = 1.4 cm, AE = 7.2 cm and AC = 1.8 cm.

(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.

(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm.

In a, P and Q are points on sides AB and AC respectively, such that . If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find AB and PQ.