Properties of Triangles RS Aggarwal Class-7 ICSE Maths Goyal Brothers Prakashan Chapter-18 Solutions. We provide step by step Solutions of Exercise / lesson-18 Properties of Triangles for ICSE Class-7 RS Aggarwal Mathematics.
Our Solutions contain all type Questions with Exe-18 A, Exe-18 B and MCQs Exe-18 C with Mental Maths to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.
| Board | ICSE |
| Publications | Goyal brothers Prakshan |
| Subject | Maths |
| Class | 7th |
| Chapter-18 | Triangles |
| Writer | RS Aggrawal |
| Book Name | Foundation |
| Topics | Solution of Exe-18 A, Exe-18 B and MCQs Exe-18 C with Mental Maths |
| Academic Session | 2021-2022 |
Properties of Triangles RS Aggarwal Class-7 ICSE Maths Goyal Brothers Prakashan Chapter-18 Solutions
-: Select Topic :-
Definition of triangle
A triangle definition states that a triangle is a polygon that consists of three sides, three edges, three vertices and the sum of internal angles of a triangle equal to 180°
Types of Triangle
| Based on the Sides | Based on the Angles |
| Scalene Triangle | Acute angled Triangle |
| Isosceles Triangle | Right angle Triangle |
| Equilateral Triangle | Obtuse-angled Triangle |
Scalene Triangle: All the sides and angles are unequal.
Isosceles Triangle: It has two equal sides. Also, the angles opposite these equal sides are equal.
Equilateral Triangle: All the sides are equal and all the three angles equal to 60°.
Acute Angled Triangle: A triangle having all its angles less than 90°.
Right Angled Triangle: A triangle having one of the three angles exactly 90°.
Obtuse Angled Triangle: A triangle having one of the three angles more than 90°.
Triangle Properties
The properties of the triangle are:
- The sum of all the angles of a triangle(of all types) is equal to 180°.
- The sum of the length of the two sides of a triangle is greater than the length of the third side.
- In the same way, the difference between the two sides of a triangle is less than the length of the third side.
- The side opposite the greater angle is the longest side of all the three sides of a triangle.
- The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property
- Two triangles are said to be similar if their corresponding angles of both triangles are congruent and lengths of their sides are proportional.
- Area of a triangle = ½ × Base × Height
- The perimeter of a triangle = sum of all its three sides
Triangle Formula
- Area of triangle is the region occupied by a triangle in a two-dimensional plane. The dimension of the area is square unit. The formula for area is given by;
Area = 1/2 x Base x Height
- The perimeter of a triangle is the length of the outer boundary of a triangle. To find the perimeter of a triangle we need to add the length of the sides of the triangle.
P = a + b + c
- Semi-perimeter of a triangle is half of the perimeter of the triangle. It is represented by s.
s = (a + b + c)/2
where a, b and c are the sides of the triangle.
- By Heron’s formula, the area of the triangle is given by:
A = √[s(s – a)(s – b)(s – c)]
where ‘s’ is the semi-perimeter of the triangle.
- By the Pythagorean theorem, the hypotenuse of a right-angled triangle can be calculated by the formula:
Hypotenuse2 = Base2 + Perpendicular2
Exe-18 A,
Properties of Triangles RS Aggarwal Class-7 ICSE Maths Goyal Brothers Prakashan
Page 196-199
Question 1:
Is it possible to form a triangle by three line segment of the following lengths ?
(i) 8 cm, 6 cm, 15 cm
(ii) ……………….
Question 2:
Is it possible to have ……………. following measures ?
(i) 25, 65, 90
(ii)………………
…………………
Question 3:
……………………..
,……………………..
………………………
Question 22:
In the given figure , ……………… ∠ACD = ∠ABE.
Question 23:
Find the unknown marked angles in each of the following figures :
(i)………………
………………..
Exe-18 B,
Properties of Triangles RS Aggarwal Class-7 ICSE Maths Goyal Brothers Prakashan
Page 204
Question 1:
In a right angled triangle, find the ………………….. 12 cm and 35 cm.
Question 2:
The length of one side of a …………………………. third side.
Question 3:
………………………
………………………
……………………..
Question 10:
State Pythagoras’s Theorem.
MCQs Exe-18 C,
Properties of Triangles RS Aggarwal Class-7 ICSE Maths Goyal Brothers Prakashan
Page 205
Choose the correct option in each of the following
Question 1:
In a triangle ABC, if ……….. is equal to
………………..
Question 2:
Two angles of a …………………. triangle measures
……………………
Question 3:
………………………..
…………………………
…………………………
Question 10:
The measure of one of the equal …………. triangle is
Mental Maths
Properties of Triangles RS Aggarwal Class-7 ICSE Maths Goyal Brothers Prakashan
Page 205
Question 1:
Fill in the blanks :
(i) In a scalene ……………
(ii) …………………
(iii)………………
(iv)………………
(v)………………
Answer :
(i) acute/different angles.
(ii) hypotenuse.
(iii) 81 degree.
(iv) 90 degree.
(v) Right angled triangle
Question 2:
Write true (T) or false (F):
(i) A triangle can have ………………….
(ii)………………
(iii)………………
(iv)………………
(v)………………
Answer :
(i) False
(ii) False
(iii) False
(iv) True
(v) False
–: End of Properties of Triangles RS Aggarwal Class-7 Solutions :–
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