Year 5 Maths: Drawing Triangles

Introduction to Triangles

Hello, Year 5! Today, we are going to learn about triangles. Triangles are shapes with three sides and three corners, which we call vertices. They are all around us, from the rooftops of houses to the shapes of sails on boats!

Types of Triangles

There are different types of triangles, and we can classify them based on their sides and angles:

1. By Sides:
   • Equilateral Triangle: All three sides are the same length. (e.g., if one side is 3 cm, all sides are 3 cm!)
   • Isosceles Triangle: Two sides are the same length, and one is different. (e.g., two sides are 4 cm, and the third side is 2 cm.)
   • Scalene Triangle: All three sides are different lengths. (e.g., one side is 5 cm, another is 3 cm, and the third is 4 cm.)
2. By Angles:
   • Acute Triangle: All angles are less than 90 degrees.
   • Right Triangle: One angle is exactly 90 degrees.
   • Obtuse Triangle: One angle is more than 90 degrees.

Drawing Triangles

Now, let’s learn how to draw triangles! Here’s a step-by-step guide.

Materials Needed:

• A ruler
• A pencil
• A protractor (for measuring angles)
• An eraser

Steps to Draw a Triangle:

1. Choose the Type of Triangle: Decide whether you want to draw an equilateral, isosceles, or scalene triangle.
2. Draw the Base: Use your ruler to draw the bottom side (base) of your triangle. For example, let’s say you want a base of 5 cm.
3. Mark the Vertices: Label the ends of your base as point A and point B.
4. Draw the Other Sides:
   • For an Equilateral Triangle, use your ruler to measure 5 cm from point A and 5 cm from point B, making sure both lines meet at the top point (point C).
   • For an Isosceles Triangle, you can choose one side to be different. For example, if AB is 5 cm, make AC 5 cm and BC 3 cm.
   • For a Scalene Triangle, you can make all sides different. Measure and connect to form the triangle.
5. Check Your Angles (if needed): If you want a specific type of triangle, use a protractor to check your angles.

Tips and Tricks

• Always use a ruler for straight lines.
• Measure carefully to keep your sides accurate.
• Use an eraser if you make a mistake.
• Practice drawing different types of triangles to get better!

Questions

Easy Level Questions (1-20)

1. How many sides does a triangle have?
2. What do we call the corners of a triangle?
3. Name one type of triangle with all sides the same length.
4. How many vertices does a triangle have?
5. What type of triangle has two equal sides?
6. What is the name of a triangle with one angle more than 90 degrees?
7. Draw an equilateral triangle with sides of 4 cm.
8. Draw a right triangle with one side of 3 cm and one side of 4 cm.
9. How many types of triangles are based on angles?
10. What do we call a triangle with all different side lengths?
11. If one side of a triangle is 6 cm and the other two sides are 6 cm, what type of triangle is it?
12. What is the sum of the angles in a triangle?
13. Draw an isosceles triangle with two sides of 5 cm and one side of 3 cm.
14. Can a triangle have two right angles? Why?
15. If a triangle has angles of 60°, 60°, and 60°, what type of triangle is it?
16. How can you check if a triangle is right-angled?
17. Draw a scalene triangle with sides of 3 cm, 4 cm, and 5 cm.
18. Can an isosceles triangle be also equilateral? Explain.
19. What is the longest side of a right triangle called?
20. If one side is 10 cm and the other two sides are 8 cm, can this form a triangle?

Medium Level Questions (21-40)

21. Draw a triangle with sides of 5 cm, 5 cm, and 7 cm. What type is it?
22. If a triangle has angles of 45°, 45°, and 90°, what type is it?
23. Can a triangle have all sides measuring 0 cm? Why or why not?
24. If two sides of a triangle are 10 cm and 10 cm, what is the minimum length of the third side?
25. Draw a triangle with a base of 6 cm and a height of 4 cm. What type is it?
26. What is the relationship between the angles of a triangle and the sides?
27. If one angle in a triangle is 100°, what can you say about the other angles?
28. Can a triangle exist with sides measuring 1 cm, 2 cm, and 3 cm? Explain.
29. Name a real-world object that resembles a triangle.
30. How would you classify a triangle with sides measuring 3 cm, 3 cm, and 4 cm?
31. What is the difference between an acute triangle and an obtuse triangle?
32. Draw a triangle and label its vertices A, B, and C. What are the angles at these points?
33. What do you call a triangle with one angle that is 90 degrees?
34. How do you know if a triangle is scalene?
35. If you increase one side of a triangle, what happens to the other sides?
36. What is the area formula for a triangle?
37. Draw an isosceles triangle with a base of 10 cm and two equal sides of 8 cm.
38. How can you tell if a triangle is isosceles by looking at it?
39. Can a triangle be both scalene and isosceles? Why?
40. If a triangle has two angles measuring 30°, what is the third angle?

Hard Level Questions (41-60)

41. Prove that the sum of the angles in a triangle is 180°.
42. Draw a triangle with sides measuring 7 cm, 24 cm, and 25 cm. What type is it?
43. If two angles in a triangle measure 35° and 65°, what is the third angle?
44. Can a triangle be formed with sides measuring 5 cm, 7 cm, and 12 cm? Explain.
45. Draw a triangle and use a protractor to measure each angle accurately.
46. What is the longest side of a triangle called, and how does it relate to the angles?
47. If a triangle is equilateral, what can you say about its angles?
48. Determine the missing angle in a triangle if the angles are 40° and 60°.
49. Can an isosceles triangle also be a right triangle? Provide an example.
50. Why is it impossible to have a triangle with two obtuse angles?
51. Draw a triangle with a base of 8 cm and a height of 5 cm. Calculate the area.
52. If a triangle has an angle of 120°, what type of triangle is it?
53. How do you find the perimeter of a triangle?
54. What is the difference between a right-angled triangle and an acute triangle?
55. Create a triangle with vertex coordinates (0, 0), (4, 0), and (2, 3). What type is it?
56. If you know two sides of a triangle are 6 cm and 8 cm, what could be the range for the third side?
57. Draw a right triangle and label the hypotenuse.
58. If the angles of a triangle are in the ratio 2:3:4, what are the measures of the angles?
59. Explain why the triangle inequality theorem is important.
60. Can a triangle have sides measuring 10 cm, 10 cm, and 20 cm? Justify your answer.

Answers Key

Easy Level Answers

1. 3
2. Vertices
3. Equilateral Triangle
4. 3
5. Isosceles Triangle
6. Obtuse Triangle
7. (Drawing example)
8. (Drawing example)
9. 3
10. Scalene Triangle
11. Isosceles Triangle
12. 180 degrees
13. (Drawing example)
14. No, because the angles must add up to 180 degrees.
15. Equilateral Triangle
16. Use a protractor to check for a 90-degree angle.
17. (Drawing example)
18. Yes, all sides can be equal.
19. Hypotenuse
20. No, because 10 is not less than 8 + 8.

Medium Level Answers

21. Isosceles Triangle
22. Right Triangle
23. No, because a triangle cannot have sides of 0 length.
24. Greater than 0 and less than 20 cm.
25. (Drawing example)
26. Larger angles opposite longer sides.
27. The other angles must be less than 80 degrees.
28. No, because 1 + 2 is not greater than 3.
29. (Various examples like roofs, pyramids)
30. Isosceles Triangle
31. Acute has all angles < 90°, obtuse has one > 90°.
32. (Drawing example)
33. Right Triangle
34. All sides are different lengths.
35. The triangle may become unbalanced.
36. Area = 1/2 × base × height
37. (Drawing example)
38. Look for the two equal sides.
39. No, they cannot have two equal sides and all different.
40. 80°

Hard Level Answers

41. Angles in a triangle always sum to 180°.
42. Right Triangle
43. 80°
44. No, because 5 + 7 is not greater than 12.
45. (Drawing example)
46. Hypotenuse; it is opposite the right angle.
47. All angles are 60°.
48. 80°
49. Yes, the right angle can be one of the equal angles.
50. Because obtuse angles are greater than 90°.
51. Area = 20 cm²
52. Obtuse Triangle
53. Perimeter = a + b + c
54. Right has one 90° angle; acute has all < 90°.
55. Scalene Triangle
56. Between 2 cm and 14 cm.
57. (Drawing example)
58. 40°, 60°, 80°
59. It prevents the formation of impossible triangles.
60. No, because 10 + 10 is not greater than 20.

That’s all for today! Keep practicing your triangles, and soon you will be a triangle master!