Properties of Triangles and the Interior and Exterior Angles of Triangles

9.2

Properties of Triangles and the Interior and Exterior Angles of Triangles

The properties of a triangle:

(i) Equilateral triangle

The number of axes of symmetry is \(3\).
All the sides are of the same length.
Every interior angle is \(60^\circ\).

(ii) Isosceles triangle

The number of axes of symmetry is \(1\).
Two of the sides have the same length.
The two base angles are of the same size.

(iii) Scalene triangle

The number of axes of symmetry is \(0\).
All the sides are of different lengths.
All the interior angles are of different sizes.

(iv) Acute-angled triangle

Every interior angle is an acute angle.

(v) Obtuse-angled triangle

One of the interior angles is an obtuse angle.

(vi) Right-angled triangle

One of the interior angles is a right angle (\(90^\circ\)).

Determine the interior angles and exterior angles of a triangle:

The sum of all the interior angles is \(180^\circ\).
The sum of an interior angle and its adjacent exterior angle is \(180^\circ\).
An exterior angle is the sum of two opposite interior angles.

Example

Calculate the value of \(x\) in the following diagram.

Noted that the sum of all the interior angles is \(180^\circ\).

Thus,

\(\begin{aligned} 37^\circ+92^\circ+x&=180^\circ \\\\129^\circ+x&=180^\circ \\\\x&=180^\circ-129^\circ \\\\&=51^\circ. \end{aligned}\)