Isosceles & Equilateral Triangles

In the study of isosceles and equilateral triangles and parallelograms, we shall recall some of the concepts discussed under congruent triangles.

Note: In geometric figures, short lines or dashes (tick marks) typically indicate that line segments or sides are of equal length.

Isosceles Triangle:

Definition: An Isosceles triangle has two equal sides. The third side is called the base . The equal sides meet at the vertex. The angle at the vertex is called the vertical angle .

The Base angles of an Isosceles Triangle are Equal

Properties of an Isosceles Triangle:

(i). Two sides equal |BA| = |CA|

(ii). Two angles equal \( \scriptsize \hat{ABD} = \hat{ACD} \)

(iii). The bisector of the vertical angle meets the base at a right angle

(iv). The bisector of the vertical angle bisects the base (i.e. |BD| = |DC| ).

Equilateral Triangle:

This is a triangle with three equal sides or it is a triangle with three angles equal (i.e. 60°).

Note that an equilateral triangle is a special isosceles triangle because all the properties of an isosceles triangle are true for an equilateral triangle.

Properties of an Equilateral Triangle:

(i). All three sides are equal (i.e. all