Isosceles Triangles
213. Two Sides, One Rule · Discovering isosceles & equilateral triangles
Dragging A changes side lengths. When two sides match, it's isosceles!
A triangle is isosceles when two sides are equal and equilateral when all three sides are equal (a special isosceles triangle). The equal sides are the legs and the third side is the base. An equilateral triangle also has all three angles equal to 60°.
What this lesson covers
Try to break it
Drag A around the canvas. The three side-length readouts shift; whenever any two of them match, the triangle is isosceles. Drag A to a position where all three come out equal — you've just made it equilateral, the special case where every pair of sides is "the equal pair".
How you build it
Construct an isosceles triangle.
- Mark point B — left end of the base.
- Mark point C — right end of the base.
- Draw the base segment BC.
- With centre B, draw an arc at any radius (this locks the compass width).
- With centre C, draw another arc of the SAME radius — the two arcs intersect above BC.
- Mark A at the intersection of the two arcs — equidistant from B and C, so AB = AC.
- Draw segment AB — the first equal side.
- Draw segment AC — the other equal side. Triangle ABC is isosceles with AB = AC.
The proof, step by step
Prove that a triangle with two equal sides is isosceles.
- Measure the lengths of all three sides of the triangle.
- A triangle with at least two equal sides is called isosceles.
- The two equal sides are the legs; the unequal third side is the base.
- If all three sides are equal, the triangle is equilateral — a special isosceles triangle.
Worked example
In triangle PQR, PQ = PR = 8 cm and QR = 6 cm. What type of triangle is PQR?
Since two sides (PQ and PR) are equal, triangle PQR is an isosceles triangle by definition.
- Equilateral
- Isosceles — correct
- Scalene
- Right-angled