Classifying 2D Figures • Topic 2 of 2

Classifying Triangles by Sides

What is a Triangle?

A triangle is a polygon with 3 sides and 3 angles. Sum of angles = 180°.

Classification by Sides:

Type	Description	Example
Equilateral	All 3 sides EQUAL	3 cm, 3 cm, 3 cm
Isosceles	2 sides EQUAL	5 cm, 5 cm, 3 cm
Scalene	NO sides equal	4 cm, 5 cm, 6 cm

Classification by Angles:

Type	Description	Example
Acute	All angles < 90°	60°, 60°, 60°
Right	One angle = 90°	30°, 60°, 90°
Obtuse	One angle > 90°	30°, 30°, 120°

TRIANGLES BY SIDES:

 EQUILATERAL ISOSCELES SCALENE
 / / /
 / / / 
 / / / 
 /______ /______ /______
 
 All sides = 2 sides = All sides
 3 equal marks 2 equal marks different


TRIANGLES BY ANGLES:

 ACUTE RIGHT OBTUSE
 / | /
 / | / 
 / | / 
 /______ |___ /______
 
 All angles One 90° One angle
 < 90° angle > 90°


COMBINING CLASSIFICATIONS:

 Triangle can have TWO names:
 
 ┌─────────────────────────────────────┐
 │ │
 │ Acute Equilateral = 60°,60°,60° │
 │ Right Isosceles = 90°,45°,45° │
 │ Obtuse Scalene = 120°,30°,30° │
 │ Acute Scalene = 50°,60°,70° │
 │ │
 └─────────────────────────────────────┘


MARKING CONVENTIONS:

 Equal sides = hash marks:
 
 /
 / Side with one mark = equal
 / Side with two marks = equal
 /______
 /
 /

 Right angle = square in corner:
 
 |
 | 
 |__

Solved Examples

Worked Example

A triangle has sides 6 cm, 6 cm, and 8 cm. How would you classify it by sides?

Solution

Two sides equal (6 and 6)
Therefore isosceles triangle
Answer: Isosceles

Worked Example

A triangle has angles 35°, 55°, and 90°. Classify by angles.

Solution

One angle = 90° (right angle)
Therefore right triangle
Answer: Right triangle

Worked Example

A triangle has sides 5 cm, 7 cm, 9 cm and angles 35°, 55°, 90°. Give both classifications.

Solution

Sides: all different → scalene
Angles: one 90° → right
Answer: Right scalene triangle

Worked Example

Can a triangle be both equilateral and right?

Solution

Equilateral = all angles 60°
Right triangle = one angle 90°
60° ≠ 90°, so impossible
Answer: No

Key Points

Equilateral = all sides equal + all angles 60°
Isosceles = 2 sides equal + 2 base angles equal
Scalene = no sides equal + all angles different
Acute = all angles < 90°
Right = one angle = 90°
Obtuse = one angle > 90°
Every triangle has TWO classifications (by sides AND by angles)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.An equilateral triangle has:

Explanation: All three equal.

Q2.An isosceles triangle has:

Explanation: Two equal sides.

Q3.A scalene triangle has:

Explanation: No equal sides.

Q4.Each angle of an equilateral triangle is:

Explanation: $60^\circ$.

Practice more MCQs → 📝 Assignment · 35 marks