Page 13 - Cambridge IGCSE Mathematics Core and Extended

D. Stating geometric properties and types of triangles

The following shows different types of triangles and their respective geometric properties. These triangles
are categorised according to the length of sides or the size of angles.
(I) According to the length of sides:
(a) Equilateral triangle

• All the sides have the same length.
• All the angles are 60°.
• It has three lines of symmetry.

(b) Isosceles triangle
• Two of the sides have the same
length.
• The base angles are equal.
• It has one line of symmetry.

(c) Scalene triangle
• All the sides have different lengths.
• All the angles are of different sizes.
• It has no lines of symmetry.

(II) According to the size of angles:
(a) Acute-angled triangle
• All the angles are acute angles.

TIPS
Many triangles could be of
(b) Obtuse-angled triangle category (I) as well as of
category (II). For example,
• One of the angles is an obtuse
angle. an equilateral triangle is also
an acute-angled triangle. A
(c) Right-angled triangle right-angled triangle could

• One of the angles is a right angle also be an isosceles triangle.
(90°). A scalene triangle could also
be an acute-angled triangle
or an obtuse-angled triangle.

E. Sum of angles of a triangle

The sum of the angles of a triangle is 180°. These angles are known as interior angles.
For example,

y
x + y + z = 180°
z
x

Chapter 11 Polygons I 153

14/07/2022 10:14 AM
DA1501_pg 147 to 161.indd 153
DA1501_pg 147 to 161.indd 153 14/07/2022 10:14 AM