Year 4 Maths: Triangles

Introduction to Triangles

Hello, Year 4! Today, we’re going to learn about triangles. A triangle is a shape that has three sides and three corners (which we call vertices). Triangles are everywhere around us! You can see them in buildings, flags, and even in the shapes of slices of pizza!

Types of Triangles

There are different types of triangles based on their sides and angles. Let’s take a look!

1. By Sides

• Equilateral Triangle: All three sides are the same length. This triangle looks very balanced!
  • Example: If each side is 5 cm, then all three sides are 5 cm.
• Isosceles Triangle: Two sides are the same length, and one side is different.
  • Example: If two sides are 4 cm each and the base is 5 cm, it’s isosceles.
• Scalene Triangle: All three sides are different lengths.
  • Example: One side is 3 cm, another is 4 cm, and the last is 5 cm.

2. By Angles

• Acute Triangle: All three angles are less than 90 degrees.
• Right Triangle: One angle is exactly 90 degrees.
• Obtuse Triangle: One angle is greater than 90 degrees.

Key Rules

• The angles in a triangle always add up to 180 degrees.
• The longest side is opposite the largest angle.
• The shortest side is opposite the smallest angle.

Tips and Tricks

• To remember the types of triangles, think about their shapes:
  • Equilateral: Equal sides and angles!
  • Isosceles: Two sides are like twins.
  • Scalene: All different, like a mixed bag of sweets.
• For angles:
  • Acute: Cute little angles (less than 90°).
  • Right: The perfect corner (exactly 90°).
  • Obtuse: An angle that’s feeling a bit too relaxed (more than 90°).

Questions

Easy Level Questions

1. How many sides does a triangle have?
2. What do we call the corners of a triangle?
3. Name a type of triangle with all sides the same length.
4. How many angles does a triangle have?
5. What is the sum of the angles in a triangle?
6. True or False: An isosceles triangle has all sides different.
7. Draw a right triangle.
8. What type of triangle has one angle greater than 90 degrees?
9. Can a triangle have two equal sides? (Yes/No)
10. What is the name of a triangle with no equal sides?

Medium Level Questions

11. If one angle of a triangle is 90 degrees and another is 30 degrees, what is the third angle?
12. Draw an equilateral triangle with sides of 6 cm.
13. What type of triangle is formed if it has angles of 60°, 60°, and 60°?
14. If a triangle has sides of 5 cm, 5 cm, and 3 cm, what type of triangle is it?
15. If the angles of a triangle are 45°, 45°, and 90°, what type of triangle is it?
16. How can you tell if a triangle is scalene just by looking at it?
17. If one side of a triangle is 8 cm, what could the lengths of the other two sides be to still form a triangle?
18. If a triangle has angles of 80°, 50°, and 50°, is it acute, right, or obtuse?
19. Draw a triangle with the following sides: 3 cm, 4 cm, and 5 cm.
20. What is the name of a triangle with two sides of 7 cm and one side of 10 cm?

Hard Level Questions

21. If a triangle has sides of 10 cm, 10 cm, and 5 cm, what type of triangle is it?
22. What is the measure of the largest angle in a triangle with sides of 6 cm, 8 cm, and 10 cm?
23. Can a triangle have two angles that are each 95 degrees? Explain why or why not.
24. If one angle in a triangle is 70° and the other two angles are equal, what are those two angles?
25. A triangle has sides of 9 cm, 12 cm, and 15 cm. Is it a right triangle? Why or why not?
26. If a triangle has angles of 30°, 30°, and 120°, what type of triangle is it?
27. Draw a triangle where the sides are in the ratio of 3:4:5. What type of triangle is it?
28. If the perimeter of an isosceles triangle is 24 cm and the base is 8 cm, what is the length of each of the equal sides?
29. Can a triangle have an angle of 0 degrees? Explain your answer.
30. If a triangle has sides of 5 cm, 12 cm, and 13 cm, prove if it is a right triangle.

Answers

Easy Level Answers

1. Three sides.
2. Vertices.
3. Equilateral triangle.
4. Three angles.
5. 180 degrees.
6. False.
7. [A right triangle drawing]
8. Obtuse triangle.
9. Yes.
10. Scalene triangle.

Medium Level Answers

11. 60 degrees.
12. [Drawing of an equilateral triangle with 6 cm sides]
13. Equilateral triangle.
14. Isosceles triangle.
15. Right triangle.
16. It has all different lengths.
17. Any two sides that add up to more than 8 cm and are less than 13 cm.
18. Acute triangle.
19. [Drawing of a triangle with sides of 3 cm, 4 cm, and 5 cm]
20. It is an isosceles triangle.

Hard Level Answers

21. Isosceles triangle.
22. 90 degrees (using the Pythagorean theorem).
23. No, because the angles would add up to more than 180 degrees.
24. Each angle would be 65 degrees (70 + 2x = 180).
25. Yes, because 9² + 12² = 15².
26. Obtuse triangle.
27. [Drawing of a triangle in the ratio 3:4:5, which is a right triangle]
28. Each of the equal sides is 8 cm.
29. No, because the angles must add up to 180 degrees.
30. Yes, because 5² + 12² = 13².

I hope you enjoyed learning about triangles! Keep practicing, and you’ll be a triangle master in no time!