These questions ask you to name a triangle, connect equal sides with equal angles, or decide whether a set of angle facts is possible. Keep the side classification and angle classification as two separate labels.
Use the requested classification axis
First underline what the question asks you to inspect: side lengths, angle sizes, or both. Compare lengths by exact equality, not by how close they seem. For angles, inspect the largest angle because one right or obtuse angle settles the angle classification. A triangle may correctly carry one name from each axis.
| Evidence | Classification and check |
|---|---|
| Three equal sides | The triangle is equilateral, which also satisfies the inclusive meaning of isosceles. If the most exact name is requested, use equilateral. |
| Exactly two equal sides | The triangle is isosceles. For lengths 8, 8 and 5, the matching pair gives the side classification. |
| Three different sides | The triangle is scalene. Lengths 5, 7 and 9 are all distinct, so no equal pair exists. |
| All three angles are smaller than a right angle | The triangle is acute-angled. For example, 47 degrees, 61 degrees and 72 degrees meet this rule and total 180 degrees. |
| One angle is a right angle | The triangle is right-angled. The remaining two angles must share the rest of the half turn. |
| One angle is greater than a right angle | The triangle is obtuse-angled. An angle of 104 degrees settles the classification even when the other two are acute. |
Use the opposite relationship when information crosses the two axes. If two angles are both 52 degrees, the sides facing those angles are equal. If three angles are equal, each is 180 divided by 3, which is 60 degrees, and the three opposite sides are equal as well.
Where classifications go wrong
| Trap | How to reject it |
|---|---|
| Choosing a broader side name when the most exact name is requested | Three equal sides meet the inclusive isosceles condition, but equilateral records all three equalities and is therefore more specific. |
| Turning one equal pair into three equal sides | Two matching lengths establish isosceles, not equilateral. Check the third length instead of extending the pattern without evidence. |
| Answering on the wrong axis | A side name does not answer a request about angles, and an angle name does not answer a request about sides. Label the requested axis before comparing names. |
| Calling a triangle acute because two angles are acute | Every triangle has at least two acute angles. The largest angle controls this classification, so inspect it before the smaller pair. |
| Treating a right angle as a default or allowing two of them | Angle sizes must fit the 180 degree total. Two right angles already use the entire total, leaving no positive third angle. |
Try it
A triangle has sides of 4 centimetres, 6 centimetres and 7 centimetres. Which name describes it by its sides?
- scalene
- isosceles
- equilateral
- obtuse-angled
A triangle is both right-angled and isosceles, so apart from its right angle its two remaining angles are equal. Enter the number of degrees in each of those two equal angles.
A triangle has angles of 90 degrees, 45 degrees and 45 degrees. Select all the names that correctly describe this triangle.
- Right-angled, because one angle is exactly 90 degrees.
- Isosceles, because two angles match and so do two sides.
- Equilateral, because a right angle counts as a third equal angle.
- Scalene, because its three angles are not all the same.