Kerala Syllabus Class 7 Mathematics - Unit 3 Triangles - Questions and Answers | Teaching Manual 

Questions and Answers for Class 7 Mathematics - Unit 3 Triangles - Study Notes | Text Books Solution STD 7 - Maths: Unit 3 Triangles - Questions and Answers | ത്രികോണങ്ങൾ - ചോദ്യോത്തരങ്ങൾ 

ഏഴാം ക്ലാസ്സ്‌  Mathematics - Unit 3 Triangles  എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്.

STD 7 - Maths: Unit 3 Triangles - Questions and Answers

♦ Textbook Activities - Page 46
♦ Draw the following figures.
• Method of construction of Figure (1)
Draw a line 3 cm long, then draw circles of radius 3 cm, centred at the endpoints. Take one of the points of intersection, say the top point, as the third corner of the triangle and erase the circle. Mark two points on each side of the triangle, 1 cm away from the corners. Joining these points, draw the second triangle. Join the opposite corners of these two triangles as we did in the previous section. The point of intersection of these lines will be the centre upon which the enclosing circle must be drawn. Finally, delete the lines joining the corners and connect the points on the sides of the triangle to the centre. Now shade the required portions as in the given picture.

• Method of construction of figure (2): This is similar to figure (1), except for the boundary. Start by drawing the two equal triangles and find the centre by joining the opposite corners, then erase the lines. Again, join the points on the sides of the triangles to the centre. Instead of a circle, enclose the entire picture inside a hexagon by connecting the corners of the triangles using lines. Colour the picture according to the given picture.
♦ Draw the following figure:
• Method of construction of figure (1):
First, draw a line. Draw two circles centred at its endpoints with radius equal to the length of the line.
Extend the line to meet the circle on the right. At that point of intersection, draw another circle with the same radius.
There are four points at which the middle circle is intersected by the other two circles. Out of those points, the top right point must be connected to the centres of the right and the middle circle, and the top left must be connected to the centres of the left and the middle circle. The two bottom points must both be connected to the centre of the middle circle. See the figure below.
Now erase the circles and shade the required portions as in the given picture.

• Method of construction of figure (2): Similar to picture (1), draw the three circles and find the four points of intersection. Connect the top two points to the centre of the middle circle, connect the bottom right point to the centres of the right and the middle circles, and connect the bottom left point to the centres of the left and the middle circles. Finally, erase the circles and give colour
♦ Lines and math
Triangles with all sides are equal. Such triangles are called equilateral triangles.
Even if the lengths of the sides are different, we can still draw the triangle if we know the three sides. Here, instead of drawing circles with equal radius, use a radius equal to the lengths of the different sides. 
• Let's look at the example of a triangle with sides 3 cm, 4 cm and 6 cm.
First, draw a line of 3 cm long. Then draw two top half of the circles centred at the endpoints, having radius 4 cm and 6 cm. Their point of intersection will be the third corner of the triangle. Joining this point to the ends of the line will give us the required triangle.

• Let's draw another triangle, with sides 6 cm, 5 cm and 7 cm.
Draw a line 6 cm long. Then, draw two small pieces of the circles centred at the endpoints, having a radius of 5 cm and 7 cm. Their point of intersection is the third corner of the triangle.
♦ Textbook Activities - Page 49 
• Now let's draw the following triangles.
Let's measure their angles,
Figure (1) - 35°, 45° and 100°
Figure (2) - 95, 50° and 35°
Figure (3) - 75°, 60° and 45°
Look at the angles and sides opposite to those angles. For example. In Figure (1), the side opposite to 100° is 7 cm, the side opposite to 45° is 5 cm, and the side opposite to 35° is 4 cm.
A similar observation done on the other triangles reveal as important fact.
In any triangle, the angles and their oppo- site sides have sizes in the same order
In a triangle, the side opposite to the largest angle is the longest, and the side opposite to the smallest angle is the shortest. If all sides are equal, all angles will also be equal, with a value of 60°. If two sides of a triangle are equal, the two angles will also be the same.
♦ Triangles and sides
We cannot draw a triangle with any three numbers as the lengths of the sides.
For eg:
To draw a triangle of sides 2 cm, 3 cm and 6 cm. We can see that after drawing a line, the circles drawn at the two endpoints do not touch each other.
In any triangle, the length of the greatest side is less than the sum of the length of the other two sides.
We can draw a triangle only when the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Example
We cannot draw a triangle with sides 10 cm, 4 cm and 5 cm. Because 4+ 5 = 9. It is less than 10.

♦ Textbook Activities - Page 52 
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? 
We cannot take 1, 2 and 3 as the third side. Because when we add these to 5, we cannot get a number greater than 8.
If we take numbers from 4 to 12. When we add smaller sides, we get a number greater than the larger side.
example, Third side = 10 cm,    5,8,10
5+8=13. It is greater than 10.
Third side = 4.    4,5,8
4+5=9. It is greater than 8.
To find this, we can use the sum and difference of the given two sides.
That is 5+8=13    8-5=3
Length of the third side is between 3 and 13. (That is numbers from 4 to 12)
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?
When we take any number from 1 to 98, the sum of the smaller sides cannot be greater than 99. For any number from 100 and above, the sum of the smaller sides cannot be greater than the larger side. Then only we can use 99.
1+99= 100             It is greater than 99
Therefore, third side = 99 cm
Another way
99+1=100. 99-1=98
The number between 98 and 100 is 99. Therefore third side is 99 cm.

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

(i) 4 cm, 6 cm, 10 cm
We cannot draw the triangle. 
Since 4+6=10.
(We can draw a triangle since it is greater than 10.) 

(ii) 3 cm, 4 cm, 5 cm.
We can draw the triangle.
(3+4=7, greater than 5.)

(iii) 10 cm, 5 cm, 4 cm
We cannot draw the triangle. 
(5+4=9, because less than 10.)

4. Draw these pictures:
• Method of construction of figure (1): We need a square with 4 cm side lengths. For this, draw a line of length 4 cm, then draw perpendiculars at the endpoints. Mark 4 cm on them and join those points to obtain the square.
Now, using these sides as a base, draw 4 triangles with 6 cm being the other two sides. Erase the remaining parts of the circles and join the corners of those triangles. Use colouring to make the figure pretty.
• Method of construction of figure (2):
(1) Draw a triangle with sides 12 cm, 10 cm and 8 cm. With 12 cm as the base.
(2) On the top corner, draw a line parallel to the base. Mark 3 cms on both sides from that corner and erase the rest. Now the parallel line is 6 cm long..
(3) Use this as the base for the next triangle, with sides 6 cm, 5 cm and 4 cm.
(4) Draw a triangle as 3 cm base on the top. Enclose the entire figure in a triangle by connecting the side corners of all three triangles.
♦ Textbook Activities - Page 56 
♦ Can you draw the following picture by joining triangles?
• Method of construction of figure (1): 
1. First, draw an equilateral triangle. 2. Divide each side into three parts.
3. Draw a hexagon by joining these points.
4. Draw 6 small triangles inside the hexagon, using its sides as their bases.
5. Join the corners of these triangles.
If we remove the lines drawn at the centre, we will get the second picture.

♦ Sides and angles.
A triangle can be drawn by knowing measure of two sides and angle between them.
• Draw the triangle of sides 4 cm and 8 cm and angle between them is 60°.
1. Draw one side of length 4 cm.
2. Make an angle 60° at one end of the line. 
3. Mark a point at this line at a distance 8 cm.
4. Join this point and the other end of the first line.
In this triangle, one angle is right-angled, ie, 90°. So this triangle is a right angled triangle. Its third angle is 30°.
A triangle of one side is two times that of the first side and one angle is 60° is a right-angled triangle.
• Draw a triangle of two sides 6 cm and 7 cm and angle between them is 40°.
Method of drawing
1. First, draw a line of length 6 cm.
2. Make an angle 40° at its one end.
3. Mark a point at a distance of 7 cm at this line from the same end.
4. Join this point and the other end of the line. If its triangle.
We can draw triangles by giving two sides and angle that are not in between them.
• Two sides are 6 cm and 4 cm and angle not in between them is 30°.
Method of drawing
1. First, draw a line of length 6 cm. 
2. Make an angle 30° at its one end.
3. Draw a circle at a distance of 4 cm from the other end.
4. Mark the points of intersection of line and circle. 
5. Join this point and the other end of the line. If its triangle.
6. Join the intersecting point and the point on the line to get a triangle.
Since the circle meets the line in two points. We get two triangles. Both of these triangles are of the above measures. However, if we use any number instead of 4 cm, we do not get two triangles. We can see that it is impossible to draw a triangle with one side of 2 cm. We can only draw a triangle if the length of the third side is greater than 6 cm.
If the third side is 3cm, we will get only one triangle, and it is a right-angled triangle.

♦ Textbook Activities - Page 60 
♦ Draw the following figures.
Method of drawing
1. Draw two triangles of sides 4 cm and two of its angles are 35°. 
Erase 1 cm length in the middle of the 4 cm line. Join the points as shown in the figure.
2. Draw an equilateral triangle of suitable measures. Mark the midpoints of its sides. Join this midpoint to the opposite corner. 
Draw suitable lines as in the figure and erase the lines which are not in the given figure.
3. Draw an equilateral triangle of suitable measures. Mark the midpoints of its sides. Join this midpoint to the opposite corner.
Draw lines parallel to the first line. Draw suitable lines as in the given figure and erase the lines which are not in the figure.
4. Draw an equilateral triangle of suitable measures. Mark the midpoints of its sides. Join this midpoint to the opposite corner. 
Draw the hexagon in the triangle by drawing suitable lines as given in the figure.
Draw 2 triangles in the hexagon. Erase the lines which are not in the given figure.