Math Core

Now that you know about angles, parallel sides and perpendicular sides, you can sort shapes like a scientist sorts animals. You look at the features a shape has, then give it the name that fits.

Sorting triangles by their angles

Every triangle has 3 angles. Look at the biggest one.

An acute triangle has 3 acute angles.
A right triangle has 1 right angle.
An obtuse triangle has 1 obtuse angle.

Left to right: an acute triangle, a right triangle and an obtuse triangle.

Tip

A triangle can never have two right angles or two obtuse angles. Try to draw one: the sides spread too far apart to ever meet. So every triangle has at least 2 acute angles.

Sorting triangles by their sides

You can also compare the lengths of the sides.

An equilateral triangle has 3 sides of the same length.
An isosceles triangle has at least 2 sides of the same length.
A scalene triangle has no sides of the same length.

Left to right: an equilateral triangle, an isosceles triangle and a scalene triangle.

Sorting quadrilaterals

For four-sided shapes, check for parallel sides, right angles (perpendicular sides) and equal sides.

Shape	Pairs of parallel sides	Right angles	Equal sides
trapezoid	at least 1	not needed	not needed
parallelogram	2	not needed	opposite sides equal
rectangle	2	4	opposite sides equal
rhombus	2	not needed	all 4 equal
square	2	4	all 4 equal

Left to right: a trapezoid, a parallelogram, a rectangle, a rhombus and a square.

A shape can have more than one name

A rectangle is a parallelogram with 4 right angles. A rhombus is a parallelogram with 4 equal sides. A square is both: it is a rectangle and a rhombus. Always look for the name that tells the most.

Worked example: Classify by angles

A triangle has angles of $90^\circ$ , $40^\circ$ and $50^\circ$ . What kind of triangle is it?

One angle is exactly $90^\circ$ , so it is a right triangle.

Worked example: Classify by sides and angles

A triangle has angles of $30^\circ$ , $30^\circ$ and $120^\circ$ , and two of its sides are the same length. Name it by its angles and by its sides.

The $120^\circ$ angle is obtuse, so it is an obtuse triangle. Two sides are equal, so it is also isosceles. It is an obtuse isosceles triangle.

Worked example: Name the quadrilateral

A quadrilateral has 2 pairs of parallel sides. It has no right angles, and its sides are not all the same length. What is its best name?

Two pairs of parallel sides make it a parallelogram. With no right angles, it can't be a rectangle or a square. With sides that are not all equal, it can't be a rhombus. Its best name is parallelogram.

Common mistake

Don't name a shape by how it is turned. A square resting on one corner still has 4 equal sides and 4 right angles, so it is still a square. Check the features, not the position.

Practice

Practice 1

A triangle has three $60^\circ$ angles. What kind of triangle is it?

Practice 2

A triangle has one angle that measures exactly $90^\circ$ . What kind of triangle is it?

Practice 3

A triangle has angles of $25^\circ$ , $35^\circ$ and $120^\circ$ . What kind of triangle is it?

Practice 4

A triangle has sides of 5 cm, 5 cm and 8 cm. What kind of triangle is it?

Practice 5

What is the best name for this shape?

Practice 6

Which sentence is always true?

Practice 7

A quadrilateral has exactly one pair of parallel sides and two right angles. What is it?

Practice 8

How many acute angles does a right triangle have?

Type a number.