Triangles
🎯 In this topic you will
- Learn the names and properties of different triangles
- Sketch different triangles
🧠 Key Words
- equilateral triangle
- isosceles triangle
- scalene triangle
Show Definitions
- equilateral triangle: A triangle in which all three sides and all three angles are equal.
- isosceles triangle: A triangle that has at least two sides of equal length and two equal angles.
- scalene triangle: A triangle in which all sides and all angles are different.
Triangles in Mathematics
T riangles are very important polygons.
Triangles and Other Shapes
T hey are useful when studying other shapes in mathematics because all polygons can be broken down into triangles.
Triangles in the Real World
T riangles are also used in architecture and building because of their strong shape.
💡 Quick Math Tip
Triangles Give Stability: A triangle cannot change shape unless one of its sides changes length, which makes it one of the strongest structures used in building and engineering.
❓ EXERCISES
1. Which of these triangles are scalene?
👀 Show answer
2. Name each type of triangle.
a. Name the triangle.
b. Name the triangle.
c. Name the triangle.
d. Name the triangle.
e. Name the triangle.
👀 Show answer
3.
a. Use a pencil and ruler to sketch an isosceles triangle.
b. Use a pencil and ruler to sketch a scalene triangle.
c. Ask your partner to check the triangles you have drawn in parts a and b. Check your partner’s triangles by tracing and comparing the sizes of the angles. Tell your partner how you know if their triangles are isosceles and scalene.
👀 Show answer
4. Which of these triangles has an obtuse angle?
👀 Show answer
5. Name the smallest triangle that has been tessellated in each pattern.
a. Name the smallest triangle.
b. Name the smallest triangle.
c. Name the smallest triangle.
👀 Show answer
6. Is it possible to draw a triangle that cannot be tessellated?
👀 Show answer
🧠 Think like a Mathematician
Explore these questions by drawing triangles and diagrams to show what is possible and what is impossible.
a. What type of triangle can have a right angle?
b. What type of triangle can have two right angles?
c. What type of triangle can have three right angles?
d. Investigate the number of acute angles and obtuse angles the different types of triangles can have. Write sentences to describe the angle properties of different types of triangles.
You are generalising when you describe which triangles are possible with each number of right angles.
You are convincing when you show which angles are possible and which are impossible in different triangles.
Show Answers
- a. A right-angled triangle can have exactly one right angle.
- b. No triangle can have two right angles, because two right angles already total $180^\circ$, leaving no angle for the third.
- No triangle can have three right angles; the angles would sum to $270^\circ$, which is impossible for a triangle.
- d. - An acute triangle has three acute angles. - A right-angled triangle has one right angle and two acute angles. - An obtuse triangle has one obtuse angle and two acute angles. It is impossible for a triangle to have more than one obtuse angle or more than one right angle because the angle sum must be $180^\circ$.