ML Aggarwal Class-7 Triangles and its Properties ICSE Maths Solutions

ML Aggarwal Class-7 Triangles and its Properties ICSE Maths Solutions Chapter-11. We provide step by step Solutions of Exercise / lesson-11 Triangles and its Properties ICSE Class-7th  ML  Aggarwal Mathematics .

Our Solutions contain all type Questions with Exe-11.1 , Exe-11.2,  Exe-11.3 , Exe-11.4, Exe-11.5 ,Objective Type Questions ( including Mental Maths Multiple Choice Questions ,  , HOTS) and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.

ML Aggarwal Class-7 Triangles and its Properties ICSE Maths Solutions Chapter-11


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Exe-11.1 ,

 Exe-11.2,

  Exe-11.3,

 Exe-11.4,

 Exe-11.5

Objective Type Questions,

Mental Maths,

Multiple Choice Questions ,(MCQ)

HOTS

Check Your Progress

 


ML Aggarwal Class-7 Triangles and its Properties ICSE Maths Solutions Exe-11.1

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Question 1.
In the adjoining figure:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q1
(i) Name the vertex opposite to side PQ.
(ii) Name the side opposite vertex Q.
(iii) Name the angle opposite to side QR.
(iv) Name the side opposite to ∠R.

Answer

In the given figure,
(i) Vertex opposite to side PQ is R.
(ii) The side opposite to the vertex Q is PR.
(iii) Angle opposite to the side QR is ∠R.
(iv) the side opposite to ∠R is PQ.

Question 2.
Look at the figures given below and classify each of the triangles according to its (a) sides (b) angles
(You may judge the nature of the angle by observation):
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q2

Answer

(i) Two sides are equal. So it is an isosceles triangle.
(ii) Three sides are unequal and one angle is 90°,
so it is a right-angled triangle end also it is a scalene triangle also.
(iii) Three sides are equal. So, it is an equilateral triangle.
(iv) Two sides are equal. So, it is an isosceles triangle.
It’s one angle is obtuse, therefore it obtuse angled triangle also.
(v) Three sides are not equal. So, it is a scalene triangle.
It’s one angle is obtuse. So, it is an obtuse angled triangle also.
(vi) Its two sides are equal and one angle is a right angle.
So it is a right-angled isosceles triangle.

Question 3.
In the given ∆PQR, if D is the mid-point of \bar { QR }, then
(i) \bar { PM } is ……..
(ii) \bar { PD } is ………
Is QM = MR?
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q3

Answer

If the given figure, in ∆PQR
D is mid-point of \bar { QR }, then
(i) PM is an altitude.
(ii) PQ is the median.
No, QM ≠ MR

Question 4.
Will an altitude always lie in the interior of a triangle? If no, draw a rough sketch to show such a case.

Answer

No, it is not necessary, it may lie outside the triangle also.
Here is given a rough sketch of the case AD is the altitude of ∆ABC.
Draw from A to the side CB (produced).
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q4

Question 5.
Can you think of a triangle in which two altitudes of the triangle is its sides? If yes, draw a rough sketch to show such a case.

Answer

Yes, it is a right-angled triangle.
Here, AB ⊥ BC and BC ⊥ AB
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q5

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Question 6.
Draw rough sketches for the following:
(i) In ∆ABC, BE is a median of the triangle.
(ii) In ∆PQR, PQ and PR are altitudes of the triangle.
(iii) In ∆XYZ, YL is an altitude in the exterior of the triangle.

Answer

(i) In ∆ABC, BE is the median of the triangle.
E is the mid-point of AC. So, BE is the median.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q6
(ii) In ∆PQR, PQ and PR are the altitudes of the triangle.
In ∆PQR, ∠P = 90°
So, PQ and PR are the altitudes.
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q6.1
(iii) In ∆XYZ, YL is the altitude in the exterior of the
triangle YL is altitude on ZX (produced).
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1 Q6.2

Question 7.
Take an equilateral triangle and draw its medians and altitudes and check that the medians and altitudes are the same.

Answer

∆ABC is an equilateral triangle.
AD, BE and CF are altitudes of the triangle.
The altitudes of an equilateral triangle
divide the sides into two equal parts.
So, altitudes are also the medians of the triangle.


Ex 11.2,  ML Aggarwal Class-7 Triangles and its Properties ICSE Maths Solutions

Question 1.
Find the value of the unknown exterior angle x in each of the following diagrams:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q1

Answer

We know that the exterior angle of a triangle
is equal to the sum of its interior opposite angles.
Therefore,
(i) Ext. ∠x = 45° + 65° = 110°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q1.1
(ii) Ext. ∠x = 55° + 40° = 95°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q1.2
(iii) Ext. ∠x = 50° + 50° = 100°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q1.3

Question 2.
Find the value of the unknown interior angle x in each of the following diagrams:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q2

Answer

We know that the exterior angle of a triangle
is equal to the sum of its interior opposite angles.
Therefore,
(i) In the given triangle,
Ext. ∠115° = x + 50°
⇒ x = 115° – 50° = 65°
⇒ x = 65°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q2.1
(ii) In given triangle,
Ext. ∠80° = 30° + x
⇒ x = 80° – 30° = 50°
⇒ x = 50°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q2.2
(iii) In given triangle,
Ext. ∠70° = x + 36°
⇒ x = 70° – 36° = 34°
⇒ x = 34°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q2.3

Question 3.
Find the value of x in each of the following diagrams:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q3

Answer

We know that the exterior angle of a triangle
is equal to the sum of its interior opposite angles.
Therefore,
(i) In a given triangle,
Ext. ∠105° = 2x + x
⇒ 3x = 105°
⇒ x = 35°
x = 35°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q3.1
(ii) In given triangle,
Ext. ∠125° = 2x + 3x
⇒ 5x = 125°
⇒ x = 25°
x = 25°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q3.2
(iii) In given triangle,
∠A + ∠B + ∠C = 180°
(Sum of angles of a triangle)
⇒ x + 60° + 50° = 180°
⇒ x + 110° = 180°
⇒ x = 180° – 110° = 70°
x = 70°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q3.3

Question 4.
Find the value of unknown x in each of the following:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q4

Answer

(i) In given triangle = Let ∆ABC
∠A + ∠B + ∠C = 180°
⇒ 50° + x + x = 180°
⇒ 2x = 180° – 50° = 130°
Hence, x = 65°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q4.1
(ii) In the given figure,
Let the name of ∆ be ABC
∠ABC + ∠ABE = 180°
⇒ ∠ABC + 110° = 180°
⇒ ∠ABC = 180° – 110° = 70°
Similarly,
∠ACB + ∠ACD = 180°
⇒ ∠ACB + 120° = 180°
⇒ ∠ACB = 180° – 120° = 60°
Now in ∆ABC
∠BAC + ∠ABC + ∠ACB = 180°
⇒ x + 70° + 60° = 180°
⇒ x + 130° = 180°
⇒ x= 180° – 130° = 50°
⇒ x = 50°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q4.2
(iii) Let the given triangle be named as ∆ABC,
where ∠C = 90°
In ∆ABC,
∠A + ∠B + ∠C = 180° (Sum of angles of a triangle)
⇒ 2x + x + 90° = 180°
⇒ 3x = 180° – 90° = 90°
⇒ x = 30°
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2 Q4.3

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