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Maths 1 Mark Question

Triangles · Maharashtra Board STD 6 (MSBSHSE - English Medium). 24 questions.

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Question 11 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Isosceles
Two angles are equal in measure.
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 21 Mark
Can a triangle have:
Two obtuse angles?
Answer
No.
For example: Let the two angles be 120° and 150°. Then, their sum will be 270°​, which cannot form a triangle.
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Question 31 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Equilateral
XY = YZ = ZX = 3cm
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 41 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Isosceles
DE = EF = 2.4cm
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 51 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Scalene
All the sides are unequal.
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 61 Mark
Fill in the blanks:
The sides of a scalene triangle are of ______ lengths.
Answer
The sides of a scalene triangle are of different lengths.
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Question 71 Mark
Fill in the blanks:
The sum of the angles of a triangle is ______.
Answer
The sum of the angles of a triangle is 180°.
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Question 81 Mark
Fill in the blanks:
A triangle has ______ sides, ______ angles and ______ vertices.
Answer
A triangle has three sides, three angles and three vertices.
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Question 91 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Equilateral
All three angles are 60°.
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 101 Mark
Fill in the blanks:
The sum of the lengths of the sides of a triangle is called its ______.
Answer
The sum of the lengths of the sides of a triangle is called its perimeter.
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Question 111 Mark
Can a triangle have:
Each angles less than $60^\circ$ ?
Answer
No.
For example: Let the two angles be $50^\circ$ and $40^\circ$, which on adding, gives $90^\circ.$
Thus, they cannot form a triangle whose third angle is $180^\circ -^90^\circ = 90^\circ​$, which^is greater than $60^\circ.$
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Question 121 Mark
Look at the figure given below. State for each triangle whether it is acute, right or obtuse.
Answer
It is an obtuse angle triangle as one angle is 130°, which is greater than 90°.
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Question 131 Mark
Look at the figure given below. State for each triangle whether it is acute, right or obtuse.
Answer
It is an acute angle triangle as all the angles in it are less than 90°.
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Question 141 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Isosceles
AC = CB = 2cm
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 151 Mark
Can a triangle have:
Each angles equal to 60°?
Answer
Yes.
For example: Sum of all angles = 60° + 60° + 60°​ = 180°.
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Question 161 Mark
Look at the figure given below. State for each triangle whether it is acute, right or obtuse.
Answer
It is an obtuse angle triangle as one angle is 92°, which is greater than 90°.
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Question 171 Mark
Draw a $\triangle\text{ABC}$. Take a point D on BC. Join AD. How many triangles do you get? Name them.
Answer
In $\triangle\text{ABC},$ D is a point on BC and AD is joined.
Now we get triangles $\triangle\text{ABC},$ $\triangle\text{ABD}$ and $\triangle\text{ADC}.$
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Question 181 Mark
In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral.
Answer
Scalene
All the angles are unequal.
Equilateral Triangle: A triangle whose all three sides are equal in length and each of the three angles measures 60°.
Isosceles Triangle: A triangle whose two sides are equal in length and the angles opposite them are equal to each other.
Scalene Triangle: A triangle whose all three sides and angles are unequal in measure.
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Question 191 Mark
Fill in the blanks:
The angles opposite to equal sides of an isosceles triangle are ______.
Answer
The angles opposite to equal sides of an isosceles triangle are equal.
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Question 201 Mark
Fill in the blanks:
Each angle of an equilateral triangle measures ______.
Answer
Each angle of an equilateral triangle measures 60°.
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Question 211 Mark
Can a triangle have:
Each angles more than $60^\circ$?
Answer
No.
For example: Let the two angles be $70^\circ$​ and $80^\circ,$ which on adding, gives $150^\circ.$
They cannot form a triangle whose third angle is $180^\circ​ - 150^\circ^= 30^\circ,$ which is less than $60^\circ.$
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Question 221 Mark
Can a triangle have:
Two right angles?
Answer
No.
For example: If the two angles are $90^\circ$ each, then the sum of two angles of a triangle will be $180^\circ$, which is not possible.
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Question 231 Mark
Look at the figure given below. State for each triangle whether it is acute, right or obtuse.
Answer
It is a right angle triangle as one angle is 90°.
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Question 241 Mark
Can a triangle have:
Two acute angles?
Answer
Yes.
For example: Let the two angles be $50^\circ$ and $60^\circ$​, which on adding, gives $110^\circ.$
They can easily form a triangle whose third angle is $180^\circ - 110^\circ = 70^\circ.$
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