Mathematics • Year 7 • Unit 3 • Lesson 2

Triangles by Sides — Real World

Classify real-world triangles by side length — yield signs, sails, A-frame tents, music stands, and bunting flags. Connect each classification to angle and symmetry properties, and justify with tick marks or measurements.

Apply · Real-World Maths

1. Word problems

Identify the side count, name the type, and add a property (symmetry or angles) where asked.

1.1 — Yield sign. A standard Australian "Give Way" yield sign has sides of length 90 cm, 90 cm and 90 cm. (a) Classify the sign by its sides. (b) What is the size of each interior angle? (c) How many lines of symmetry does it have? 3 marks

Stuck? All sides equal → equilateral; angle sum 180° split into 3 equal parts.

1.2 — Racing sail. A racing sail has sides 4 m, 6 m, and 7 m. (a) Classify by sides. (b) How many lines of symmetry does it have, and how many equal angles? (c) Why might a sail-maker deliberately design a sail with no equal sides? 3 marks

Stuck on (c)? Think about how wind hits different parts of the sail.

1.3 — A-frame tent. An A-frame tent has two equal sloping poles of 2.5 m each, and a floor of 2 m forming the third side of the triangle visible from the end. (a) Classify by sides. (b) How many lines of symmetry, and where does it run? (c) If the angle the floor makes with one pole is 64°, what is the angle the floor makes with the other pole? Justify. 3 marks

Stuck on (c)? Equal sides force equal base angles.

1.4 — Music-stand top. The triangular top of a music stand has measurements 30 cm, 30 cm and 30 cm. (a) Classify by sides. (b) State each interior angle. (c) Briefly explain why the maker chose this shape (in terms of symmetry). 3 marks

Stuck? Three equal sides → equilateral; 3 lines of symmetry — looks the same from every direction.

1.5 — Bunting flags. A party banner has triangular bunting flags. Five of the flags have sides 12 cm, 12 cm, 8 cm. Three flags have sides 10 cm, 10 cm, 10 cm. Two flags have sides 7 cm, 9 cm, 11 cm. (a) Classify each type of flag. (b) How many flags in total are isosceles? Equilateral? Scalene? 3 marks

Stuck? Classify each flag type by counting equal sides, then count how many flags of that type.

2. Explain your thinking

Use full sentences. 4 marks

2.1 A classmate looks at a triangle that "looks like" it has two equal sides and immediately writes "isosceles." There are no tick marks and no measurements on the diagram. Explain in your own words (i) why eyeballing a triangle is not enough to classify it, (ii) what specific information they should look for instead, and (iii) why the words "diagrams are not drawn to scale" matter in geometry. Refer to tick marks somewhere in your answer.

Stuck? Revisit lesson § "Spot the Trap" — count the ticks, don't trust the picture.

How did this worksheet feel?

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Yield sign 90, 90, 90 cm

(a) All sides equal → equilateral. (b) Each angle = 180 ÷ 3 = 60°. (c) 3 lines of symmetry.

1.2 — Racing sail 4, 6, 7 m

(a) No equal sides → scalene. (b) 0 lines of symmetry; 0 equal angles. (c) A scalene sail catches wind differently along each edge, giving the sail-maker independent control over its lift and drag in different conditions.

1.3 — A-frame tent 2.5, 2.5, 2 m

(a) Two equal sides → isosceles. (b) 1 line of symmetry, running from the top (apex, where the two 2.5 m poles meet) straight down to the middle of the 2 m floor. (c) The two angles opposite the two equal sides are equal (base angles), so the other floor-to-pole angle is also 64°.

1.4 — Music-stand top 30, 30, 30 cm

(a) Equilateral. (b) Each angle = 60°. (c) An equilateral triangle has 3 lines of symmetry, so the stand looks identical from any of the three sides — the music sheet can be turned and still fit symmetrically, and the design is visually balanced.

1.5 — Bunting flags

(a) Five flags 12, 12, 8 → isosceles; three flags 10, 10, 10 → equilateral; two flags 7, 9, 11 → scalene.
(b) Total: isosceles 5, equilateral 3, scalene 2. (Sum = 10 flags ✓.)

2.1 — Explain your thinking (sample response)

Eyeballing a triangle isn't enough because diagrams in geometry are rarely drawn perfectly to scale — a triangle that looks like it has two equal sides may actually be scalene. To classify properly, the classmate should look for tick marks (small dashes on each side: sides with the same number of ticks are equal in length) or for stated side measurements. The "not drawn to scale" warning matters because it tells you the picture is for layout only, not measurement. The maths must come from the symbols and numbers, not from the appearance. Without ticks or measurements, no classification can be made.

Marking: 1 for naming the visual problem; 1 for mentioning tick marks; 1 for "diagrams not to scale" explanation; 1 for clear full-sentence answer.

HSCScience • Mathematics • Year 7 • Unit 3 • Lesson 2 • Worksheet 2 (Apply)