Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles

Triangles Exercise 15A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Stale, if the triangles are possible with the following angles :
(i) 20°, 70° and 90°
(ii) 40°, 130° and 20°
(iii) 60°, 60° and 50°
(iv) 125°, 40° and 15°
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 1

Question 2.
If the angles of a triangle are equal, find its angles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 2
Question 3.
In a triangle ABC, ∠A = 45° and ∠B = 75°, find ∠C.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 3

Question 4.
In a triangle PQR, ∠P = 60° and ∠Q = ∠R, find ∠R.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 4

Question 5.
Calculate the unknown marked angles in each figure :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A Q5
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 5

Question 6.
Find the value of each angle in the given figures:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 6

Question 7.
Find the unknown marked angles in the given figure:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 7
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 8

Question 8.
In the given figure, show that: ∠a = ∠b + ∠c
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A Q8
(i) If ∠b = 60° and ∠c = 50° ; find ∠a.
(ii) If ∠a = 100° and ∠b = 55° : find ∠c.
(iii) If ∠a = 108° and ∠c = 48° ; find ∠b.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 9

Question 9.
Calculate the angles of a triangle if they are in the ratio 4 : 5 : 6.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 10

Question 10.
One angle of a triangle is 60°. The, other two angles are in the ratio of 5 : 7. Find the two angles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 11

Question 11.
One angle of a triangle is 61° and the other two angles are in the ratio 1\(\frac { 1 }{ 2 }\) : 1 \(\frac { 1 }{ 3 }\). Find these angles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 12

Question 12.
Find the unknown marked angles in the given figures :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A Q12
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 13
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 14
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15A 15

Triangles Exercise 15B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the unknown angles in the given figures:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 16
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 17
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 18

Question 2.
Apply the properties of isosceles and equilateral triangles to find the unknown angles in the given figures :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 19
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 20
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 21
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 22

Question 3.
The angle of vertex of an isosceles triangle is 100°. Find its base angles.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 23

Question 4.
One of the base angles of an isosceles triangle is 52°. Find its angle of vertex.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 24

Question 5.
In an isosceles triangle, each base angle is four times of its vertical angle. Find all the angles of the triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 25

Question 6.
The vertical angle of an isosceles triangle is 15° more than each of its base angles. Find each angle of the triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 26

Question 7.
The base angle of an isosceles triangle is 15° more than its vertical angle. Find its each angle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 27

Question 8.
The vertical angle of an isosceles triangle is three times the sum of its base angles. Find each angle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 28

Question 9.
The ratio between a base angle and the vertical angle of an isosceles triangle is 1 : 4. Find each angle of the triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 29

Question 10.
In the given figure, BI is the bisector of∠ABC and Cl is the bisector of ∠ACB. Find ∠BIC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q10
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 30
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 31

Question 11.
In the given figure, express a in terms of b.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q11
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 32

Question 12.
(a) In Figure (i) BP bisects ∠ABC and AB = AC. Find x.
(b) Find x in Figure (ii) Given: DA = DB = DC, BD bisects ∠ABC and∠ADB = 70°.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q12
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 33
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 35

Question 13.
In each figure, given below, ABCD is a square and ∆ BEC is an equilateral triangle.
Find, in each case : (i) ∠ABE(ii) ∠BAE
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q13
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 36
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 37

Question 14.
In ∆ ABC, BA and BC are produced. Find the angles a and h. if AB = BC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B Q14
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15B 38

Triangles Exercise 15C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Construct a ∆ABC such that:
(i) AB = 6 cm, BC = 4 cm and CA = 5.5 cm
(ii) CB = 6.5 cm, CA = 4.2 cm and BA = 51 cm
(iii) BC = 4 cm, AC = 5 cm and AB = 3.5 cm
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 39
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 40
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 41

Question 2.
Construct a A ABC such that:
(i) AB = 7 cm, BC = 5 cm and ∠ABC = 60°
(ii) BC = 6 cm, AC = 5.7 cm and ∠ACB = 75°
(iii) AB = 6.5 cm, AC = 5.8 cm and ∠A = 45°
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 42
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 43

Question 3.
Construct a ∆ PQR such that :
(i) PQ = 6 cm, ∠Q = 60° and ∠P = 45°. Measure ∠R.
(ii) QR = 4.4 cm, ∠R = 30° and ∠Q = 75°. Measure PQ and PR.
(iii) PR = 5.8 cm, ∠P = 60° and ∠R = 45°.
Measure ∠Q and verify it by calculations
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 44
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 45
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 46

Question 4.
Construct an isosceles A ABC such that:
(i) base BC = 4 cm and base angle = 30°
(ii) base AB = 6-2 cm and base angle = 45°
(iii) base AC = 5 cm and base angle = 75°.
Measure the other two sides of the triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 47
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 48
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 49

Question 5.
Construct an isosceles ∆ABC such that:
(i) AB = AC = 6.5 cm and ∠A = 60°
(ii) One of the equal sides = 6 cm and vertex angle = 45°. Measure the base angles.
(iii) BC = AB = 5-8 cm and ZB = 30°. Measure ∠A and ∠C.
Solution:


Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 50
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 51
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 52

Question 6.
Construct an equilateral A ABC such that:
(i) AB = 5 cm. Draw the perpendicular bisectors of BC and AC. Let P be the point of intersection of these two bisectors. Measure PA, PB and PC.
(ii) Each side is 6 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 53
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 54

Question 7.
(i) Construct a ∆ ABC such that AB = 6 cm, BC = 4.5 cm and AC = 5.5 cm. Construct a circumcircle of this triangle.
(ii) Construct an isosceles ∆PQR such that PQ = PR = 6.5 cm and ∠PQR = 75°. Using ruler and compasses only construct a circumcircle to this triangle.
(iii) Construct an equilateral triangle ABC such that its one side = 5.5 cm.
Construct a circumcircle to this triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 55
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 56
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 57
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 58
Question 8.
(i) Construct a ∆ABC such that AB = 6 cm, BC = 5.6 cm and CA = 6.5 cm. Inscribe a circle to this triangle and measure its radius.
(ii) Construct an isosceles ∆ MNP such that base MN = 5.8 cm, base angle MNP = 30°. Construct an incircle to this triangle and measure its radius.
(iii) Construct an equilateral ∆DEF whose one side is 5.5 cm. Construct an incircle to this triangle.
(iv) Construct a ∆ PQR such that PQ = 6 cm, ∠QPR = 45° and angle PQR = 60°. Locate its incentre and then draw its incircle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 59
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 60
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 61
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 62
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 15 Triangles Ex 15C 63

Selina Concise Mathematics Class 7 ICSE Solutions

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