Mathematics • Year 7 • Unit 3 • Lesson 2
Types of Triangles by Their Sides
Build fluency classifying triangles by side lengths: equilateral (3 equal), isosceles (2 equal), scalene (0 equal). Read tick marks confidently, link side-equality to equal opposite angles, and state lines of symmetry (3, 1 and 0 respectively).
1. I do — fully worked example
Read every line. The reason on the right explains why side-equality forces equal opposite angles.
Problem. A triangle has sides 8 cm, 8 cm and 5 cm. Classify it by its sides, state the number of lines of symmetry, and say what you can conclude about its angles.
Step 1 — Count equal sides.
8 = 8, but 8 ≠ 5 → exactly two sides equal
Reason: count the matches — not eyeballing.
Step 2 — Name the type.
Two equal sides → isosceles
Reason: "iso" = same; two sides the same.
Step 3 — Lines of symmetry.
Isosceles → 1 line of symmetry
Reason: it runs from the apex (where the two 8 cm sides meet) down to the middle of the 5 cm base.
Step 4 — What we know about the angles.
The two angles opposite the 8 cm sides are equal (base angles).
Reason: equal sides → equal opposite angles.
Answer: Isosceles; 1 line of symmetry; two equal base angles opposite the 8 cm sides.
2. We do — fill in the missing steps
Faded working — fill the blanks. 4 marks
Problem. A triangle has all three sides marked with one tick each. Classify the triangle, state the size of every interior angle, and the number of lines of symmetry.
Step 1 — Read the ticks: all three sides have one tick → all three sides are ____________ in length.
Step 2 — Name the type: three equal sides → ____________________.
Step 3 — Find each angle:
Each angle = 180 ÷ ____ = ____°
Step 4 — Lines of symmetry: ____ lines.
3. You do — independent practice
Show the side count, the type name, and (where asked) the symmetry. First four are foundation, middle two standard, last two extension.
Foundation — name the type
3.1 Classify a triangle with sides 6 cm, 6 cm, 6 cm. 1 mark
3.2 Classify a triangle with sides 5 cm, 7 cm, 10 cm. 1 mark
3.3 Classify a triangle with sides 9 cm, 9 cm, 4 cm. 1 mark
3.4 A triangle has one tick on two of its three sides. Which type is it, and how many lines of symmetry does it have? 1 mark
Standard — link sides to angles
3.5 An isosceles triangle has one base angle of 55°. What is the other base angle, and why? 2 marks
3.6 A triangle has three different side lengths. How many lines of symmetry does it have, and how many equal angles? 2 marks
Extension — push your thinking
3.7 A student claims "Every equilateral triangle is also isosceles." Decide whether this statement is true or false, and explain in one or two sentences why we still name it equilateral. 2 marks
3.8 A triangle has sides 12 cm, 12 cm and 12 cm. (a) Name its type. (b) State each interior angle. (c) State the number of lines of symmetry. (d) Describe where each line of symmetry runs. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — All three sides one tick each
Step 1: equal. Step 2: equilateral. Step 3: each angle = 180 ÷ 3 = 60°. Step 4: 3 lines.
3.1 — 6, 6, 6
All three sides equal → equilateral.
3.2 — 5, 7, 10
5 ≠ 7 ≠ 10 → no equal sides → scalene.
3.3 — 9, 9, 4
Exactly two sides equal → isosceles.
3.4 — Two sides have one tick each
Two equal sides → isosceles; 1 line of symmetry (from the apex down to the middle of the third side).
3.5 — Isosceles with one base angle 55°
The other base angle = 55° (the two angles opposite the two equal sides are equal — base angles of an isosceles triangle).
3.6 — Three different sides
That's scalene → 0 lines of symmetry and 0 equal angles.
3.7 — Every equilateral is also isosceles?
True. An equilateral triangle has three equal sides, so it certainly has at least two equal sides, which is the isosceles condition. However, we always use the most specific name available — "equilateral" gives more information (all three equal, not just two), so we use it instead of the broader "isosceles" label.
3.8 — 12, 12, 12
(a) Equilateral. (b) Each angle = 180 ÷ 3 = 60°. (c) 3 lines of symmetry. (d) Each line runs from one vertex straight to the midpoint of the opposite side — there are three such lines, one for each vertex.