🧱 See It
A triangle can be sorted in two completely separate ways, and it always gets one name from each list — like how a person can be both "tall" and "left-handed" at the same time.
The first way looks only at the side lengths: are they all different, are two the same, or are all three the same? The second way looks only at the corners (angles): is there a square corner, a corner wider than square, or are all the corners narrow? The two questions don't affect each other — you answer them one at a time.
✏️ Draw It
Sorting by sides. The little tick marks are the trick: sides with the same number of ticks are the same length.
Scalene — all three sides different lengths (no ticks match).
Isosceles — exactly two sides equal (the two ticked sides match; the base is different).
Equilateral — all three sides equal (every side has a matching tick).
Sorting by corners. Read the biggest corner of each triangle — that one alone decides the name.
Acute — every corner is narrower than a square corner (all under 90°).
Right — one corner is exactly a square corner (90°). The little square is the signal to look for.
Obtuse — one corner is wider than a square corner (over 90°). Only one corner can ever be this wide.
🔢 Write It
Name #1 — by sides:
| Name | Rule |
|---|---|
| Scalene | all three sides different |
| Isosceles | exactly two sides equal |
| Equilateral | all three sides equal |
Name #2 — by angles:
| Name | Rule |
|---|---|
| Acute | all three angles less than 90° |
| Right | one angle exactly 90° |
| Obtuse | one angle greater than 90° |
💡 Worked Examples
Example 1 — Sides 5 cm, 5 cm, 8 cm. What name by sides?
- Are all three the same? No.
- Are exactly two the same? Yes — the two 5 cm sides.
- Answer: Isosceles
Example 2 — Angles 40°, 60°, 80°. What name by angles?
- Find the biggest angle: 80°.
- Is it exactly 90°? No. More than 90°? No. So the biggest corner is still under 90°.
- Answer: Acute (every angle is under 90°)
Example 3 — Give BOTH names: sides all different, angles 30°, 55°, 95°.
- By sides: all three different → Scalene.
- By angles: biggest is 95°, which is more than 90° → Obtuse.
- Answer: a scalene obtuse triangle — one name from each list.
Example 4 — Does turning a triangle change its name?
- Rotate a right triangle so its square corner points down, or sideways, or any direction at all.
- The side lengths didn't change, and the corner sizes didn't change — only which way it's facing.
- Answer: No. A triangle is classified by its sides and angles alone, regardless of orientation — a tipped-over right triangle is still a right triangle.