Isoceles Triangle — free printable diagram

What is an isosceles triangle?

An isosceles triangle has at least two sides of equal length. The two angles opposite those equal sides — the base angles — are equal as well. The third angle can be anything, as long as all three still add to 180°.

Sides

3

Equal sides

At least 2

Equal angles

At least 2 (the base angles)

Angles add up to

180°

Lines of symmetry

1 (3 if equilateral)

Rotational symmetry

Order 1 (order 3 if equilateral)

• The equal angles sit opposite the equal sides. That is the fact most isosceles questions turn on: given the apex angle a, each base angle is (180° − a) ÷ 2.
• Working backwards, if you know one base angle b, the apex angle is 180° − 2b.
• It has one line of symmetry, running from the apex down to the midpoint of the base, which means folding along that line matches the two halves exactly.
• Definitions differ here, so check your syllabus: most define isosceles as “at least two equal sides”, which makes every equilateral triangle isosceles as well. Some primary schemes teach “exactly two”, which excludes the equilateral case.
• An isosceles triangle can also be right-angled — a right isosceles triangle has angles of 90°, 45° and 45°.