Week 26 · Triangles and quadrilaterals · 3 lessons
1
Triangles by their angles and sides
Discover Mathematics P4: Term 2, Unit 12, Lessons 11–14
GoalSort triangles by their angles (acute, right, obtuse) and by their sides (equilateral, isosceles, scalene).
New words
equilateral triangle · a triangle with 3 equal sidesisosceles triangle · a triangle with at least 2 equal sidesscalene triangle · a triangle with no equal sides
Explanation
A triangle has 3 sides and 3 angles, and we can sort triangles in two ways. By angles: an acute triangle has three acute angles, a right triangle has one right angle, and an obtuse triangle has one obtuse angle. A triangle can have only one right or obtuse angle, because the other two angles have to be acute. By sides: an equilateral triangle has 3 equal sides, an isosceles triangle has at least 2 equal sides, and a scalene triangle has no equal sides. In drawings, small tick marks on sides show that they are equal. Both ways of sorting can be used for the same triangle, for example a right isosceles triangle, which is half of a square.
Worked examples
Sort by angles. The first triangle has three angles smaller than a square corner: acute. The second has a square corner, marked with a small square: right. The third has one angle wider than a square corner: obtuse.
Sort by sides. The first triangle has one tick on each of its 3 sides: all equal, so it is equilateral. The second has two sides with two ticks: those 2 are equal, so it is isosceles. The third has sides of three different lengths: scalene.
Use both ways for one triangle. This triangle has a right angle and two equal sides (the ticks), so it is a right isosceles triangle. A triangle cut from a square corner to the opposite corner is exactly like this.
Class activity
Triangle sort. Cut out six triangles from paper: an equilateral one, two isosceles ones, and three more of different shapes. Measure the sides with a ruler and test the angles with a paper corner. Put each triangle in a box of a two-way table: acute, right or obtuse across; equilateral, isosceles or scalene down.
Practice
1
Name this triangle by its sides.
Isosceles: two sides are 6 cm.
2
A triangle has sides 7 cm, 7 cm and 7 cm. Name it by its sides. What kind of angles does it have?
Equilateral. All three angles are acute.
3
A triangle has sides 4 cm, 5 cm and 6 cm. Is it equilateral, isosceles or scalene?
Scalene: no two sides are equal.
4
How many acute angles are there in a right triangle?
Two. One angle is right, so the other two are acute.
5
Mina says a triangle can be both right and isosceles. Is she right?
Yes. A triangle with a right angle and two equal sides exists, for example the one cut from a square along its diagonal.
