Discover Mathematics P5: Term 2, Unit 10, Lessons 1–4
GoalMeasure the sides of a triangle and name it by its sides and by its angles.
New words
equilateral · a triangle with 3 equal sidesisosceles · a triangle with 2 equal sidesscalene · a triangle with no equal sidesobtuse angle · an angle greater than a right angle
Explanation
We can name a triangle in two ways. By its sides: measure all three sides with a ruler. If all three are equal it is equilateral, if exactly two are equal it is isosceles, and if all three are different it is scalene. By its angles: compare each angle with a right angle (the corner of a book). If all three angles are smaller than a right angle the triangle is acute. If one angle is a right angle it is a right triangle. If one angle is bigger than a right angle it is obtuse. A triangle has only one right or obtuse angle at most. The two names go together: a triangle can be both isosceles and right, or both scalene and obtuse. An equilateral triangle always has three equal angles of 60°, so it is acute.
By sides
By angles
equilateral: 3 equal sides
acute: all angles smaller than a right angle
isosceles: 2 equal sides
right: one right angle
scalene: no equal sides
obtuse: one angle bigger than a right angle
Worked examples
Measure: 4 cm, 4 cm, 4 cm. All three sides are equal, so the triangle is equilateral. Its three angles are equal, so it is also acute.
Measure: 5 cm, 5 cm, 6 cm. Exactly two sides are equal, so it is isosceles. All its angles are smaller than a right angle, so it is acute.
Measure: 3 cm, 4 cm, 5 cm. No two sides are equal, so it is scalene. The corner between the 3 cm and 4 cm sides fits a right angle, so it is a right triangle.
Class activity
Straw triangles. Cut straws or paper strips of lengths 3, 4, 4, 5, 5, 5 and 6 cm. Choose three strips, lay them as a triangle and decide: equilateral, isosceles or scalene? Is any corner a right angle (test with the corner of a book)? Can you choose three strips that do NOT make a triangle? (Try 3, 4 and 8 if you have a longer strip.)
Practice
1
A triangle has sides 7 cm, 7 cm and 3 cm. Name it by its sides.
Isosceles.
2
A triangle has three sides of 8 cm. Name it by its sides.
Equilateral.
3
A triangle has angles 40°, 60° and 80°. Is it acute, right or obtuse?
Acute: all three angles are smaller than 90°.
4
A triangle has angles 30°, 40° and 110°. Is it acute, right or obtuse?
Obtuse: one angle (110°) is bigger than 90°.
5
A square piece of paper is cut along a diagonal. Describe the two triangles by their sides and by their angles.
Each triangle has two equal sides (the sides of the square), so it is isosceles. It has a right angle (the corner of the square), so it is a right triangle.
