Geometry · Ordinary Level
Isosceles & Equilateral
Ordinary Level · Class 4 · Tap NEXT to begin
Section 1 of 2
Isosceles Triangles
Two equal sides → two equal angles
In an isosceles triangle, the two equal sides sit opposite two equal base angles.
Worked example — find the base angles
An isosceles triangle has an apex angle of $70^\circ$ and two equal base angles $A$. Find $A$.
$A + A + 70 = 180 \Rightarrow 2A + 70 = 180$
$2A = 110 \Rightarrow A = 55^\circ$
$A = 55^\circ$
Worked example — using an exterior angle
An isosceles triangle has a base angle of $40^\circ$ (its exterior angle is $140^\circ$) and apex angle $A$. Find $A$.
Both base angles are $40^\circ$ (isosceles)
$A + 40 + 40 = 180 \Rightarrow A = 100^\circ$…
or from the apex split: $A = 180 - 140 = 40$, giving $2\times$ base; here $A = 100^\circ$
$A = 100^\circ$
Section 2 of 2
Equilateral Triangles
All equal
In an equilateral triangle all three sides are equal and all three angles are $60^\circ$.
Worked example — all sides equal
Show each angle of an equilateral triangle ($x$, $x$, $x$) is $60^\circ$.
$x + x + x = 180 \Rightarrow 3x = 180$
$x = 60^\circ$
$x = 60^\circ$
You try
A triangle has angles $70^\circ$, $50^\circ$ and $A$. Find $A$.
They add to $180$.
$70 + 50 = 120$
$A = 180 - 120 = 60^\circ$
$A = 60^\circ$
That’s Class 4.
Isosceles (two equal base angles) and equilateral ($60^\circ$ each). Class 5: right-angled triangles and Pythagoras.