Two sides equal — and here's the magic: the angles opposite those sides are equal too. Those are the base angles.
Drag the corners
isosceles · acute
angles sum ≈ 180°
The isosceles facts
- The two equal sides are the legs; the odd one out is the base.
- Base angles are equal — the two angles touching the base.
- The line from the apex to the middle of the base is an axis of symmetry: it's also the perpendicular bisector of the base, the angle bisector at the apex, and the altitude — all the same line.
- An equilateral triangle is just a *very* even isosceles triangle (every pair of sides is equal).
Your turn
An isosceles triangle has an apex angle of 40°. What are the two base angles?
Watch out
Don't assume the *given* angle is the apex. If a problem says 'an isosceles triangle has an angle of 40°' it could be a base angle (then the angles are 40°, 40°, 100°) or the apex (40°, 70°, 70°). Two valid triangles!
Recap
- Two equal sides ⇒ two equal base angles (and vice-versa).
- The apex-to-base midline is symmetry axis, bisector, and altitude in one.
- Watch out: a single given angle can lead to two different isosceles triangles.