Triangles and Their Properties Class 6 ICSE

 

Worksheet 1 

Triangles and Their Properties

A. Multiple Choice Questions (MCQs)

1. A triangle has _______ sides.
   a) 2
   b) 3
   c) 4
   d) 5

2. The sum of the angles of a triangle is always:
   a) 90°
   b) 180°
   c) 360°
   d) 270°

3. A triangle with all sides equal is called:
   a) Scalene triangle
   b) Isosceles triangle
   c) Equilateral triangle
   d) Right-angled triangle

4. In a right-angled triangle, the side opposite the right angle is called the:
   a) Median
   b) Base
   c) Hypotenuse
   d) Altitude

5. A triangle with one angle greater than 90° is called:
   a) Right-angled triangle
   b) Acute-angled triangle
   c) Obtuse-angled triangle
   d) Scalene triangle

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B. Fill in the Blanks

1. The sum of the lengths of any two sides of a triangle is always _______ than the length of the third side.
2. A triangle with two equal sides is called a/an _______ triangle.
3. The longest side of a right-angled triangle is the _______.
4. The altitude of a triangle is a line segment drawn from a vertex to the _______ side.
5. A triangle with all angles less than 90° is called a/an _______ triangle.

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C. True or False

1. The sum of all angles in a triangle is 180°.
2. An equilateral triangle has all angles equal to 90°.
3. In a scalene triangle, all sides are of different lengths.
4. An obtuse triangle has three obtuse angles.
5. The perpendicular drawn from a vertex to the opposite side is called the median.

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D. Match the Following

Column A	Column B
1. Equilateral triangle	a. All angles are less than 90°
2. Scalene triangle	b. One angle is 90°
3. Acute-angled triangle	c. All sides are equal
4. Right-angled triangle	d. No sides are equal
5. Obtuse-angled triangle	e. One angle is greater than 90°

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E. Short Answer Questions

1. Define a triangle.
2. What is the Pythagoras Theorem? Write its formula.
3. Write the three types of triangles based on the length of their sides.
4. Explain what an altitude of a triangle is.
5. How do you classify triangles based on their angles?

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F. Solve the Following Problems

1. In a triangle, two angles measure 40° and 60°. Find the third angle.
2. Check whether the following lengths can form a triangle: 5 cm, 6 cm, and 12 cm.
3. Find the length of the hypotenuse of a right-angled triangle if the other two sides measure 6 cm and 8 cm.
4. A triangle has angles 70°, 50°, and 60°. Is it an acute-angled triangle?

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G. Activity-Based Question

Draw and Measure:

1. Draw a triangle with sides 5 cm, 6 cm, and 7 cm using a ruler and compass.
2. Measure and write down the angles using a protractor.
3. Classify the triangle based on its sides and angles.

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H. Higher Order Thinking Skills (HOTS)

1. Can a triangle have two right angles? Why or why not?
2. A triangle has sides 8 cm, 15 cm, and 17 cm. Prove whether it is a right-angled triangle using the Pythagoras Theorem.

Worksheet 2

The Triangle and Its Properties

A. Fill in the Blanks

1. A triangle with all three sides of different lengths is called a _______ triangle.
2. The line segment joining a vertex of a triangle to the midpoint of the opposite side is called a _______.
3. If one angle of a triangle is 90°, the triangle is called a _______ triangle.
4. The sum of the lengths of two sides of a triangle is always _______ than the third side.
5. The angle opposite the longest side of a triangle is always the _______ angle.

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B. Multiple Choice Questions (MCQs)

1. What is the sum of the three angles of a triangle?
   a) 90°
   b) 180°
   c) 270°
   d) 360°

2. In an isosceles triangle:
   a) All sides are equal
   b) All angles are different
   c) Two sides are equal
   d) Two angles are obtuse

3. Which of the following can be the sides of a triangle?
   a) 2 cm, 2 cm, 5 cm
   b) 4 cm, 5 cm, 6 cm
   c) 1 cm, 2 cm, 3 cm
   d) 7 cm, 2 cm, 10 cm

4. A triangle with one angle greater than 90° is called a:
   a) Right triangle
   b) Acute triangle
   c) Obtuse triangle
   d) Equilateral triangle

5. How many medians does a triangle have?
   a) 1
   b) 2
   c) 3
   d) 4

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C. True or False

1. The perpendicular bisector of a triangle always passes through a vertex.
2. The longest side of a right-angled triangle is called the hypotenuse.
3. A triangle can have more than one obtuse angle.
4. In an equilateral triangle, all sides and angles are equal.
5. The sum of two angles of a triangle can be less than the third angle.

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D. Short Answer Questions

1. What is a median of a triangle? Draw a diagram to explain.
2. State and explain the Triangle Inequality Property with an example.
3. How can you determine whether a triangle is acute, obtuse, or right-angled by using its angles?
4. Why can’t a triangle have more than one right angle?
5. Classify the following triangles based on their sides:
   a) 7 cm, 7 cm, 7 cm
   b) 5 cm, 12 cm, 13 cm
   c) 6 cm, 6 cm, 8 cm

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E. Match the Following

Column A	Column B
1. Triangle Inequality Rule	a. All sides and angles are equal
2. Right-angled triangle	b. Sum of two sides > third side
3. Scalene triangle	c. Hypotenuse is the longest side
4. Equilateral triangle	d. All sides of different lengths
5. Altitude	e. Perpendicular from vertex to side

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F. Solve These Problems

1. Find the Third Angle:
   In a triangle, two angles are 45° and 65°. Find the third angle and classify the triangle based on its angles.

2. Check the Triangle Property:
   Can a triangle be formed with sides 8 cm, 6 cm, and 14 cm? Justify your answer using the triangle inequality property.

3. Find the Height:
   In an equilateral triangle with side length 10 cm, find the height using the formula:

   $$\text{Height} = \frac{\sqrt{3}}{2} \times \text{Side length}$$
   

4. Pythagoras Theorem:
   A right-angled triangle has one side 9 cm and another side 12 cm. Find the hypotenuse using the Pythagoras theorem.

5. Word Problem:
   A triangle has angles in the ratio 2:3:4. Find the measure of each angle and state the type of triangle based on its angles.