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}

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}