R d sharma solutions mathematics class 10 Solutions for Chapter 3 triangles

Exercises in Chapter 3 triangles Grade 10

Exercise 4.1

Exercise 4.2

Exercise 4.3

Exercise 4.4

Exercise 4.5

Questions in Exercise 4.1

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 their 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 are and their corresponding sides are (b) (equal, proportional).

Questions in Exercise 4.2

In a Δ ABC, D and E are points on the sides AB and AC respectively such that DE || BC.

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

ii) If AD/DB = 3/4 and AC = 15 cm, Find AE.

iii) If AD/DB = 2/3 and AC = 18 cm, Find AE.

iv) If AD = 4 cm, AE = 8 cm, DB = x – 4 cm 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 AD/BD = 4/5 and EC = 2.5 cm, Find AE.

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

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

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

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

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

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

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

ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 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 Δ ABC, D and E are points on AB and AC respectively, such that DE ∥ BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm. Find BD and CE.

Questions in Exercise 4.3

In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D.

(i) if BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC

(ii) if BD = 2 cm, AB = 5 cm, and DC = 3 cm, find AC.

(iii) if AB = 3.5 cm, AC = 4.2 cm, and DC = 2.8 cm, find BD.

(iv) if AB = 10 cm, AC = 14 cm, and BC = 6 cm, find BD and DC.

In figure 4.57, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm, and BC = 12 cm, find CE.

Questions in Exercise 4.4

(i) In fig. 4.70, if AB∥CD, find the value of x.

(ii) In fig. 4.71, if AB∥CD, find the value of x.

(iii) In fig. 4.72, if AB ∥ CD. If OA = 3x – 19, OB = x – 4, OC = x- 3 and OD = 4, find x.

Questions in Exercise 4.5