L2 · Triangles by Side and by Angle

Learning goal

“I can give a triangle TWO names: one name from its side lengths (equilateral, isosceles, or scalene) and one name from its angles (right, acute, or obtuse).”

Equilateral triangle — a triangle with all three sides equal in length.

Isosceles triangle — a triangle with exactly two sides equal in length (in this unit, "two equal sides" triangles whose third side is different).

Scalene triangle — a triangle with no sides equal in length; all three sides are different.

Right angle — a square corner: the benchmark angle (90°) that triangle angle names are measured against. A triangle with one right angle is a right triangle.

Worked example

A triangle has sides 5 cm, 5 cm, 8 cm. Step 1: Count the equal sides. Two sides match (5 and 5); the third is different. Step 2: All three equal -> equilateral. Exactly two equal -> isosceles. None equal -> scalene. Step 3: This triangle's side name is isosceles. Second example: sides 6 cm, 7 cm, 9 cm - no matches at all -> scalene. Say it plainly: the side name is decided by counting matches among the three measurements. Nothing else.

Check yourself — explain it

Why is a triangle with sides 5, 5, 8 NOT equilateral?

Paired problem — example still visible

Name this triangle by side: sides 9 cm, 9 cm, 9 cm -> Equilateral

Faded completion — last step is yours

"Sides 4, 6, 4: two sides match, so the side name is ___" -> isosceles

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz