Types Of Triangles - GCSE Maths - Steps, Examples & Worksheet - Free Printable

The image you've uploaded is a table summarizing the properties of different types of triangles. It categorizes triangles based on their sides and angles, providing both visual representations and key characteristics.

Let’s go through each triangle type, explain its properties, and clarify any potential confusion:

---

1. Equilateral Triangle

- Image: A triangle with all three sides marked as equal (tick marks), and all angles indicated as equal.
- Properties:
- All three sides are equal in length.
- All three angles are equal, each measuring 60°.
- ✔ This is a special case where symmetry is perfect: equilateral = equiangular.

---

2. Isosceles Triangle

- Image: A triangle with two sides marked as equal (tick marks) and two base angles shaded or marked as equal.
- Properties:
- Two sides are equal in length.
- The angles opposite the equal sides are also equal.
- Note: It can have one obtuse angle (if the apex angle is greater than 90°).
- 🔍 Example: If two sides are 5 cm and the base is 8 cm, the two base angles will be equal.

---

3. Scalene Triangle

- Image: A triangle with no equal sides or angles shown.
- Properties:
- No sides are equal.
- No angles are equal.
- Can contain one obtuse angle.
- There are two subtypes:
- Acute scalene: All angles < 90°.
- Obtuse scalene: One angle > 90°.
- 🔍 Example: Sides of 3 cm, 4 cm, and 6 cm → all different → scalene.

---

4. Right-Angled Triangle

- Image: A triangle with a small square at one corner indicating a 90° angle.
- Properties:
- Contains one right angle (90°).
- The side opposite the right angle is called the hypotenuse (longest side).
- Follows the Pythagorean theorem: $ a^2 + b^2 = c^2 $, where $ c $ is the hypotenuse.
- 📌 Not necessarily isosceles — unless specified.

---

5. Right Isosceles Triangle

- Image: A right triangle with two equal sides and two equal angles (both 45°).
- Properties:
- One right angle (90°).
- Two equal sides (legs).
- Two equal angles of 45° each.
- So: $ 45^\circ + 45^\circ + 90^\circ = 180^\circ $ — satisfies triangle angle sum.
- 🔍 Special case: Combines both right angle and isosceles properties.

---

Summary Table Recap

| Triangle Type | Equal Sides | Equal Angles | Right Angle? | Notes |
|----------------------|-------------|--------------|--------------|-------|
| Equilateral | 3 | 3 | No | All angles = 60° |
| Isosceles | 2 | 2 | No (can be) | Can have an obtuse angle |
| Scalene | 0 | 0 | No (can be) | All sides/angles differ |
| Right-Angled | 0 or more | 0 or more | Yes | One 90° angle |
| Right Isosceles | 2 | 2 (45°) | Yes | Special hybrid |

---

Key Takeaways:

- Triangles can be classified by sides (equilateral, isosceles, scalene) or by angles (acute, right, obtuse).
- Some triangles fit into multiple categories (e.g., right isosceles).
- The sum of interior angles in any triangle is always 180°.

This table is excellent for learning how to identify and classify triangles based on visual and geometric features.

Let me know if you'd like practice problems or help identifying a specific triangle!