Mathematics Solutions Solutions for Class 6 Maths Chapter 15 Triangles And Their Properties are provided here with simple step-by-step explanations. These solutions for Triangles And Their Properties are extremely popular among Class 6 students for Maths Triangles And Their Properties Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 6 Maths Chapter 15 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 6 Maths are prepared by experts and are 100% accurate.
Page No 80:
Question 1:
Observe the figures below and write the type of the triangle based on its angles.
Answer:
In △PQR, ∠Q = 90∘ (a right angle)
Therefore, △PQR is a right angle traingle.
In △XYZ, ∠Y = 125∘ (an obtuse angle)
Therefore, △XYZ is an obtuse angle traingle.
In △LMN, all angles are acute angles.
Therefore, △LMN is a acute angle traingle.
Page No 80:
Question 2:
Observe the figures below and write the type of the triangle based on its sides.
Answer:
In △ABC, all sides are equal.
Therefore, △ABC is an equilateral traingle.
In △DEF, all sides are different.
Therefore, △DEF is a scalene traingle.
In △UVQ, two sides are equal.
Therefore, △UVW is an isosceles traingle.
Page No 80:
Question 3:
As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is
shorter? Explain why.
Answer:
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, in △ABC, AC < AB + BC.
Hence, the shortest way to reach school is via AC.
Page No 80:
Question 4:
The lengths of the sides of some triangles are given. Say what types of triangles they are.
(1) 3 cm, 4 cm, 5 cm (2) 3.4 cm, 3.4 cm, 5 cm
(3) 4.3 cm, 4.3 cm, 4.3 cm (4) 3.7 cm, 3.4 cm, 4 cm
Answer:
(1)
All sides are different.
Therefore, it is a scalene traingle.
(2)
Two sides are equal.
Therefore, it is an isosceles traingle.
(3)
All sides are equal.
Therefore, it is an equilateral traingle.
(4)
All sides are different.
Therefore, it is a scalene traingle.
Page No 80:
Question 5:
The lengths of three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
(1) 17 cm, 7 cm, 8 cm (2) 7 cm, 24 cm, 25 cm
(3) 9 cm, 6 cm, 16 cm (4) 8.4 cm, 16.4 cm, 4.9 cm
(5) 15 cm, 20 cm, 25 cm (6) 12 cm, 12 cm, 16 cm
Answer:
(1) 17 cm, 7 cm, 8 cm
Here, 17 > 7 + 8 or 17 > 15
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is not possible.
(2) 7 cm, 24 cm, 25 cm
Here, 7 < 24 + 25 or 7 < 49
24 < 7 + 25 or 24 < 32
25 < 7 + 24 or 25 < 31
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is possible.
(3) 9 cm, 6 cm, 16 cm
Here, 16 > 9 + 6 or 16 > 15
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is not possible.
(4) 8.4 cm, 16.4 cm, 4.9 cm
Here, 16.4 > 8.4 + 4.9 or 16.4 > 13.3
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is not possible.
(5) 15 cm, 20 cm, 25 cm
Here, 15 < 20 + 25 or 15 < 45
20 < 15 + 25 or 20 < 40
25 < 15 + 20 or 25 < 35
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is possible.
(6) 12 cm, 12 cm, 16 cm
Here, 12 < 12 + 16 or 12 < 28
12 < 12 + 16 or 12 < 28
16 < 12 + 12 or 16 < 24
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the traingle is possible.
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