Mathematics • Year 7 • Unit 3 • Lesson 2
Triangles by Sides — Mixed Challenge
Bring together everything from Lesson 2: side classification, tick marks, symmetry, and the link between equal sides and equal opposite angles. Spot a common error and tackle an open-ended sketching puzzle.
1. Mixed problems — choose the right rule
Mix classifying, tick reading, symmetry counting and side-angle linking. 2 marks each
1.1 Classify the triangle with sides 5 cm, 12 cm, 13 cm.
1.2 A triangle has all sides marked with one tick each. State (a) the type and (b) each interior angle.
1.3 An isosceles triangle has base angles of 70° each. Without using the angle sum yet, what can you say about the third angle (apex)? Then check by finding its value.
1.4 A triangle has two sides of length 8 cm with one tick each, and a third side with no tick. Classify it.
1.5 A triangle has sides 6 cm, 8 cm, 10 cm. (a) Classify by sides. (b) State the number of lines of symmetry.
1.6 Explain why an equilateral triangle has more lines of symmetry than an isosceles triangle.
2. Find the mistake
Another Year 7 student tried to classify a triangle. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's problem: A triangle has sides 7 cm, 7 cm and 7 cm. Classify it and state its lines of symmetry.
Line 1: Two of the sides are equal (7 = 7).
Line 2: Two equal sides → isosceles.
Line 3: Isosceles has 1 line of symmetry. Answer: isosceles, 1 line.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? Count again — how many sides equal 7? Use the MOST specific name available.3. Open-ended challenge — sketch and classify
This question has many correct answers. Use a ruler to draw, and label with tick marks. 4 marks
3.1 In the space below (or on a separate sheet), sketch each of the following triangles using a ruler and pencil. Add the correct number of tick marks to each side so that the type is unmistakable. Label each one.
- An isosceles triangle with two sides 7 cm and a third side 4 cm.
- An equilateral triangle with each side 5 cm.
- A scalene triangle with sides 4 cm, 6 cm and 7 cm.
Then state for each one: (a) the number of lines of symmetry, (b) how many of its angles are equal.
Bonus: Can you draw a triangle that is BOTH a right-angled triangle (one 90° angle) AND isosceles? Add it to your sketches and write down what the three angles must be.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 5, 12, 13
All sides different → scalene.
1.2 — All sides one tick each
(a) Equilateral. (b) Each angle = 180 ÷ 3 = 60°.
1.3 — Isosceles, base angles 70° each
The apex angle is the third angle of the triangle, opposite the unequal third side. Using angle sum: 180 − 70 − 70 = 40°.
1.4 — Two sides 8 cm, one tick each; third side untick'd
Two equal sides marked → isosceles (the third side is different, hence no matching tick).
1.5 — 6, 8, 10
(a) Scalene. (b) 0 lines of symmetry.
1.6 — Why more lines of symmetry?
An equilateral triangle has all three sides equal AND all three angles equal, so every vertex behaves identically — you can fold from each of the three vertices straight through to the midpoint of the opposite side and the two halves match. That gives 3 lines of symmetry. An isosceles triangle has only two sides equal, so only ONE special vertex (the apex) sits at the head of a fold-line — the other two vertices are different from each other. That gives only 1 line of symmetry.
2 — Find the mistake
(a) The mistake is on Line 1 (and carries through to Line 2 and Line 3).
(b) The student only counted two of the sides as equal, but actually all three sides equal 7 cm (7 = 7 = 7). The most specific name for "all three sides equal" is equilateral, not isosceles.
(c) Corrected working:
Line 1: All three sides are equal (7 = 7 = 7).
Line 2: Three equal sides → equilateral.
Line 3: Equilateral has 3 lines of symmetry. Answer: equilateral, 3 lines.
3 — Open-ended sketch (sample marking key)
Isosceles 7-7-4: One tick on each of the two 7 cm sides (no ticks on the 4 cm side). (a) 1 line of symmetry. (b) 2 equal angles (the two base angles).
Equilateral 5-5-5: One tick on each side (all three). (a) 3 lines of symmetry. (b) 3 equal angles, each 60°.
Scalene 4-6-7: No ticks needed (all sides different). (a) 0 lines of symmetry. (b) 0 equal angles.
Bonus — right isosceles: One 90° angle, plus two equal sides forcing two equal angles. The two remaining angles must add to 180 − 90 = 90, and they are equal, so each is 45°. Angles: 45°, 45°, 90°.
Marking: 1 for each correctly-sketched + ticked triangle (3 marks total); 1 for fully correct (a) and (b) on all three; bonus credited for any valid right-isosceles sketch with 45-45-90 labelled.