Students often refer to Kerala State Syllabus SCERT Class 7 Maths Solutions and Class 7 Maths Chapter 3 Triangles Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 7 Maths Chapter 3 Solutions Triangles
Class 7 Maths Chapter 3 Triangles Questions and Answers Kerala State Syllabus
Triangles Class 7 Questions and Answers Kerala Syllabus
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Question 1.
The sides of a triangle are natural numbers. If the lengths of two sides are 5 centimetres and 8 centimetres, what are the possible numbers which can be the length of the third side?
Answer:
We know that the sum of the lengths of any two sides is greater than the length of the third side.
So, 5 + 8 should be greater than the third side.
That is, 13 is greater than the third side.
So, the length of the third side should be less than 13.
Also, we know that the difference of the lengths of any two sides is smaller than the length of the third side.
So, 8 – 5 should be less than the third side.
3 should be lesser than the third side.
So, the length of the third side should be something greater than 3.
The natural numbers greater than 3 and lesser than 13 are; 4, 5, 6, 7, 8, 9, 10, 11 and 12.
These are the possible numbers that can be the length of the third side.
Question 2.
The lengths of the sides of a triangle are all natural numbers and two of the sides are 1 centimetre and 99 centimetres. What is the length of the third side?
Answer:
We know that the sum of the lengths of any two sides is greater than the length of the third side.
So, 1 + 99 should be greater than the third side.
That is, 100 is greater than the third side.
So, the length of the third side should be less than 100.
Also, we know that the difference of the lengths of any two sides is smaller than the length of the third side.
So, 99 – 1 should be less than the third side.
98 should be less than the third side.
So, the length of the third side should be something greater than 98.
The natural number greater than 98 and lesser than 100 is 99.
Thus the length of the third side is 99 cm.
Question 3.
Which of the following sets of three lengths can be used to draw a triangle?
(i) 4 centimetres, 6 centimetres, 10 centimetres
(ii) 3 centimetres, 4 centimetres, 5 centimetres
(iii) 10 centimetres, 5 centimetres, 4 centimetres
Answer:
(i) 4 + 6 = 10, which is not greater than the third side. So, it is not possible to draw a triangle with these lengths.
(ii) Here, the sum of any two sides is greater than the third side. So, we can draw a triangle with this set of lengths.
(iii) 5 + 4 = 9, which is not greater than the third side. So, it is not possible to draw a triangle with these lengths.
Question 4.
Draw these pictures:
(i)
Answer:
Steps to draw:
- Draw a square of side length 4 cm. (You can use the compass and the protractor)
- Draw the triangles of length 6 cm, 6 cm and 4 cm on all four sides of the square. (Measure 6 cm on your compass and draw an arc from each end of the sides of the square. join the meeting point of the arc’ to both ends of the sides)
- Join the third vertices of all the triangles.
(ii)
Answer:
Steps to draw:
- Draw a triangle of sides 12 cm, 10 cm, and 8 cm.
- Draw a triangle of sides 6 cm, 5 cm, and 4 cm. (Make sure that the midpoint of the side of length 6 cm is the upper vertex of the first triangle)
- Draw a triangle of sides 3 cm, 2.5 cm, and 2 cm. (Make sure that the midpoint of the side of length 3 cm is the upper vertex of the second triangle)
- Draw a line passing through the left vertices of all the triangles.
- Draw a line passing through the right vertices of all the triangles.
Intext Questions and Answers
Question 1.
Try to draw the pictures below:
(i)
Answer:
Step 1: Draw a triangle with equal side lengths as discussed above. (You are free to choose the side length)
Step 2: Extend the bottom side of the triangle to the right.
Step 3: Draw an equilateral triangle with this new line as the base.
Step 4: Draw the third triangle as shown in the figure.
Step 5: Delete the circles.
(ii)
Step 1: Draw a triangle with equal side lengths as discussed. (You are free to choose the side length)
Step 2: Draw a line of length the same as the side length of the triangle as shown in the figure.
Step 3: Draw an equilateral triangle with this new line as the base.
Step 4: Draw a line of length the same as the side length of the triangle as shown in the figure.
Step 5: Draw an equilateral triangle with this new line as the base.
Step 6: Delete the circles.
Question 2.
How do we draw a triangle with all its sides are equal?
Answer:
Let’s do it with the help of an example. Suppose we want to draw a triangle with all its sides equal to 3 cm. Following are the steps to draw it.
Step 1: Draw a line of length 3 cm
Step 2: Draw a circle with a radius of 3 cm (length of the given line) from the right end of the line.
Step 3: Draw a circle with a radius of 3 cm (length of the given line) from the left end of the. line.
Step 4: Both the circles intersect at two points. Choose any of them as the third vertex and complete the triangle.
Step 5: Delete the circles. Thus, we get the required triangle.
Question 3.
Draw the following triangle using circles.
Answer:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.
Question 4.
Can you draw these pictures by joining more and more small triangles?
Answer:
Draw two equilateral triangles of the same size as shown below.
Join all the outer vertices.
Draw the lines as shown.
Erase the unnecessary lines.
Consider the marked points.
Join the opposite points.
Shade it as shown in the text.
Question 5.
Draw the following figures using the methods we have used in this lesson.
Answer:
(i) Step 1:
Step 2:
Step 3:
Step 4:
(ii) Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
(iii) Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
(iv) Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Class 7 Maths Chapter 3 Kerala Syllabus Triangles Questions and Answers
Question 1.
Which one of the following measures can be the sides of a triangle
(a) 3 cm, 4 cm, 7 cm
(b) 6 cm, 7 cm, 14 cm
(c) 4 cm, 5 cm, 10 cm
(d) 4 cm, 5 cm, 8 cm
Answer:
a) 3+4=7. It is not greater than the third side. So, it is not possible to draw such a triangle.
b) 6+7=13. It is not greater than the third side. So, it is not possible to draw such a triangle.
c) 5+49. It is not greater than the third side. So, it is not possible to draw such a triangle.
d) The sum of the lengths of any two sides is greater than the third side. So, it is possible to draw such a triangle.
Question 2.
Zeenath doing a project to find out the measures which can be used to draw a triangle. Which among the following measures can be used to draw a triangle?
(a) 8 cm 4 cm 3 cm
(b) 9 cm 5 cm 12 cm
(c) 5 cm 5 cm 10 cm
(d) 6 cm 7 cm 15 cm
Answer:
a) 4+37. It is not greater than the third side. So, it is not possible to draw such a triangle.
b) The sum of the lengths of any two sides is greater than the third side. So, it is possible to draw such a triangle.
c) 5+5 10. It is not greater than the third side. So, it is not possible to draw such a triangle.
d) 6+7=13. It is not greater than the third side. So, it is not possible to draw such a triangle.
Question 3.
Can a triangle have sides with lengths 6 cm, 5 cm and 9 cm?
Answer:
6 + 5 = 11
6 + 9 = 15
5 + 9 = 14
Here, sum of any two sides is greater than the third side.
Thus, a triangle can have sides with lengths 6 cm, 5 cm and 9 cm.
Question 4.
Is it possible to have a triangle with the following sides?
(i) 3 cm, 4 cm and 7 cm.
(ii) 7 cm, 7 cm and 7 cm.
(iii) 2 cm, 4 cm and 2 cm.
(iv) 3 cm, 5 cm and 7 cm.
Answer:
(i) 3 + 4 = 7, which is not greater than the third side. So, triangle is not possible.
(ii) All sides equal means equilateral triangle. An equilateral triangle can be of any length. So, triangle is possible.
(iii) 2 + 2 = 4, which is not greater than the third side. So, triangle is not possible.
(iv) 3 + 5 = 8
3 + 7 = 10
5 + 7 = 12
Here, sum of any two sides is greater than the third side. So, triangle is possible.
Question 4.
Draw the right triangle whose sides are 4 cm, 12 cm and 10 cm.
Answer:
Class 7 Maths Chapter 3 Notes Kerala Syllabus Triangles
We are already familiar with the concept of triangles. This chapter introduces a new idea called an equilateral triangle. We will also discuss how to draw different triangles using circles.
Following are the main topics discussed in this chapter.
Steps to draw an equilateral triangle using circles
- Draw a line of the given length
- Draw a circle with the same radius from the right end of the line.
- Draw a circle with the same radius from the left end of the line.
- Choose the intersecting point as the third vertex of the triangle
Steps to draw a non-equilateral triangle using circles
- Draw a line of length same as the first side of the triangle.
- Draw a semicircle with the length of the second side as the radius from one end of the line.
- Draw a semicircle with the length of the third side as the radius radius from other end of the line.
- Choose the intersecting point of these two circles as the third vertex of the triangle.
Relation between sides of the triangles
In any triangle;
the sum of the lengths of any two sides greater than the length of the third side.
the difference of the lengths of any two sides is smaller than the length of the third side.
Other ideas
A triangle having all three sides of the same length is called an equilateral triangle.
Sum of all the angles in a triangle is 180°
If only two angles are given we can draw more than one triangle with these.
If the length of two sides and the angle between them is specified, then there is only one triangle with this measure.
Lines And Math
Triangles with all sides equal are called equilateral triangles.
Eg:
In an equilateral triangles, all angles are equal to 60°
How can we draw triangles with unequal sides using circles?
Step 1: Draw a line of length same as the first side of the triangle.
Step 2: Draw a semicircle with the length of the second side as the radius from one end of the first line.
Step 3: Draw a semicircle with the length of the third side as the radius from the other end of the line.
Step 4: Choose the intersecting point of these two semi circles as the third vertex draw a triangle.
Relation between the length of sides of a triangle.
In any triangle;
the sum of the lengths of any two sides is greater than the length of the third side.
the difference of the lengths of any two sides is smaller than the length of the third side.
Angle Math
Sum of all the angles in a triangle is 180°
The total measure of the three angles of a triangle is 180°. This is called the angle sum property of a traingles
We can draw several triangles with two specified angles.
Eg:
To draw a specific triangle, we have to specify not only two angles, but the length of the side on which they stand also.
To draw more than one triangle with the same angles it is enough to draw lines parallel to the sides of the first triangle.
Eg:
Sides And Angles
If we specify the lengths of two sides of a triangle and the angle between them, we have the triangle. In a triangle with angles 30°, 60°, and 90°, the larger side is two times the smaller sides.
Eg:
How do we draw a triangle with all its sides are equal?
- Triangles with all sides equal are called equilateral triangles.
- How do we draw triangles with unequal sides using circles?
- In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.
Relation between the length of sides of a triangle.
In any triangle;
- the sum of the lengths of any two sides is greater than the length of the third side.
- the difference of the lengths of any two sides is smaller than the length of the third side.
- Sum of all the angles in a triangle is 180°
- We can draw several triangles with two specified angles.
- To draw a specific triangle, we have to specify not only two angles, but the length of the side on which they stand also.
- If we specify the lengths of two sides of a triangle and the angle between them, we have the triangle.
In a triangle with angles 30°, 60°, and 90o, the larger side is two times the smaller sides.