Triangles • Topic 1 of 3

Classification of Triangles and Angle Properties

What is a Triangle? A triangle is a closed figure with three sides, three angles, and three vertices. It is the simplest polygon.

Classification by Sides:

Type	Description	Example
Scalene triangle	All three sides are different lengths	Sides: 3cm, 4cm, 5cm
Isosceles triangle	At least two sides are equal	Sides: 5cm, 5cm, 4cm
Equilateral triangle	All three sides are equal	Sides: 6cm, 6cm, 6cm

Classification by Angles:

Type	Description	Example
Acute triangle	All angles < 90°	Angles: 50°, 60°, 70°
Right triangle	One angle = 90°	Angles: 30°, 60°, 90°
Obtuse triangle	One angle > 90°	Angles: 120°, 30°, 30°

Angle Sum Property: The sum of the three interior angles of any triangle is 180°.

\[ \angle A + \angle B + \angle C = 180^\circ \]

Exterior Angle Property: An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

\[ \text{Exterior angle} = \text{Sum of two remote interior angles} \]

Solved Examples

Worked Example

Classify the triangle with sides 7 cm, 7 cm, and 5 cm.

Solution- Two sides are equal (7 cm and 7 cm) - Third side is different (5 cm) - This is an **isosceles triangle - **Answer:** Isosceles triangle *Example 2: In a triangle, two angles are 45° and 65°. Find the third angle. Solution: - Using angle sum property: $45° + 65° + \angle C = 180°$ - $110° + \angle C = 180°$ - $\angle C = 70°$ - **Answer:** 70° *Example 3: Find the exterior angle at vertex C if $\angle A = 50°$ and $\angle B = 70°$. Solution: - Exterior angle at C = $\angle A + \angle B$ (remote interior angles) - $= 50° + 70° = 120°$ - **Answer:** 120°

Key Points

Scalene: all sides different | Isosceles: two sides equal | Equilateral: all sides equal
Acute: all angles < 90° | Right: one angle = 90° | Obtuse: one angle > 90°
Angle sum property: $\angle A + \angle B + \angle C = 180°$
Exterior angle property: Exterior angle = sum of two remote interior angles
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Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The angle sum of a triangle is:

Explanation: Always $180^\circ$.

Q2.Each angle of an equilateral triangle is:

Explanation: $60^\circ$.

Q3.An exterior angle equals the sum of the two:

Explanation: Opposite interior angles.

Q4.A scalene triangle has:

Explanation: All different.

Practice more MCQs → 📝 Assignment · 35 marks