Std 6 th Mathematics- 15. Triangles and their Properties
Question 1:
Observe the figures below and write the type of the triangle based on its angles.
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Answer 1:
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.
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.
Question 2:
Observe the figures below and write the type of the triangle based on its sides.
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Answer 2:
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.
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.
Question 3:
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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 3:
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.
Therefore, in △ABC, AC < AB + BC.
Hence, the shortest way to reach school is via AC.
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
(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 4:
(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.
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.
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
(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 5:
(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.
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.
Std 6 th Mathematics- 15. Triangles and their Properties
![Std 6 th Mathematics- 15. Triangles and their Properties]()
Reviewed by Amol Uge
on
January 09, 2019
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