Constructing Triangles from Given Measurements

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Construct the Triangle in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a triangle sketched with three side lengths marked on it: 6 cm along the bottom, 4 cm up one side and 5 cm up the other. If two of you were each handed those same three lengths and told to build the triangle, would you both end up with the exact same shape, or could you build different-looking triangles? Hands up: what is your gut feeling?

Teacher Notes

Take three hands-up answers, not open call-outs. Don't resolve it yet — the whole lesson settles this. Hold the suspense: let's see by the end whether you were right.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~11 mins

Watch the board build each triangle from three given sides. The circle tool swings an arc at a set distance, just like your compass: draw the base, swing an arc from each end, and the crossing point is the third corner. Watch where the arcs cross, and watch what happens when they can't.

Teacher Notes

Name the three moves each time: draw the base, swing both arcs, join the crossing point.

6, 5, 4: arcs cross at one point only above the base. Ask why that fixes the shape.

5, 5, 5: both arcs same radius, corner lands centrally. This is the equilateral, every side equal.

7, 6, 5: same procedure, new numbers. Reassure the method never changes.

2, 2, 9: the non-example. 9 cm base, two 2 cm arcs. Trace both arcs with your finger so the class sees them fall short. They never meet, so no triangle.

Draw out the rule in plain words: the two shorter sides must add up to more than the longest, or the arcs never cross. Here 2 + 2 is far short of 9. This previews the maths-talk at the end.

STE link if useful: same set-and-swing skill as technical drawing and marking out a frame in woodwork.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~8 mins

Today we build triangles from three given sides together on the board. We will work through three sets in turn: first 5 cm, 4 cm and 3 cm; then 6 cm, 6 cm and 4 cm; then 5 cm, 5 cm and 5 cm. Each time a pupil swings the two compass arcs from each end of the base and joins where they cross, and we check together that the triangle closes from exactly those three sides.

Build a triangle from three sides

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Run the circle tool. Work through three sets in turn, starting with the sides on screen (5, 4, 3), then 6, 6, 4, then 5, 5, 5: set the base, then let a pupil swing each arc and join the crossing point. Ask the class each time: did the arcs cross? where? does the triangle close? Rotate three or four pupils across the sets. Watch for the slip of setting the compass to the wrong length before swinging.

+15 XP

4 - Construct the Triangle in Your Copy ~6 mins

COPYBOOK MOMENT

In your maths copy, construct the SSS triangle with sides 6 cm, 5 cm and 4 cm using your own ruler and compass. Draw the 6 cm base first, then swing an arc of 5 cm from one end and an arc of 4 cm from the other, and join where they cross. Label each side with its length. Take your time — a steady, smooth arc beats a fast one.

Teacher Notes

Give pupils enough time to finish one full construction without rushing — for many this is their first hands-on compass triangle. Walk the room glancing at compass technique — point planted firmly, arc swung in one smooth move. This is whole-class copybook practice, not marking. Catch the common slip of the compass slipping wider mid-swing. Pupils who find the base line tricky can use the compass_construction_sheet with the base already drawn, so they focus on the arcs only.

+10 XP

5 - Class Challenge ~11 mins

We'll build four triangles together on the interactive, one at a time, each a bit harder than the last. Take turns at the board: set the base, swing both arcs, join where they cross. Check the sides match before we move on.

Build four triangles from given sides

Teacher Notes

Pupils take turns at the board; class confirms each before pressing on. Keep it brisk.

Each triangle is built on screen the way it is built on paper: set the compass with the slider, tap to set the base, swing an arc from each end, then join where the arcs cross. Tap Check before moving on, then Next for the following triangle. If a pupil mis-sets the compass, Undo step takes the last line back without losing the rest.

First: sides 4 cm, 4 cm, 4 cm. Base 4 cm, both arcs 4 cm. Watch where they cross.

Second: sides 5 cm, 5 cm, 5 cm. The compass stays on 5 cm the whole way. Ask what is special about the two arc radii here (both the same as the base).

Third: sides 5 cm, 4 cm, 3 cm. Base 5 cm, then arcs 4 cm and 3 cm from each end. Resetting the compass between the two arcs is the step pupils forget.

Closing challenge: sides 7 cm, 6 cm, 5 cm. Larger numbers, same three steps.

+10 XP

6 - What Did We Notice? ~6 mins

MATHS TALK

Earlier on the board we saw sides of 2 cm, 2 cm and 9 cm. One pupil says those will make a long thin triangle. Another says it can never make a triangle at all. Who is right, and what did the compass arcs show us?

Teacher Notes

Listen for pupils reasoning that the two short arcs (2 cm and 2 cm) can never reach far enough to cross when the base is 9 cm — point back to the on-screen non-example from Watch and Notice where the arcs fell short. Revoice: so the two shorter sides have to add up to more than the longest side, or the arcs never meet. Connect back to the Getting Started question — the right three sides fix one unique triangle, but the wrong three sides fix none.

+10 XP

7 - What's Next ~4 mins

Key Takeaways

To construct an SSS triangle: draw the base, swing an arc from each end set to the other two sides, and join where they cross.
The right three side lengths fix one unique triangle — everyone who measures carefully gets the same shape.
Some side lengths cannot form a triangle: the two shorter sides must add up to more than the longest side, or the arcs never meet.

Coming up

Next we pick up the protractor and learn to measure angles accurately, the skill we will need to construct triangles from sides and angles together.

Teacher Notes

Keep this brisk. Recap the three construction steps once more and flag that the protractor is the next tool to master.

+5 XP

Pupil practice

Module 7 · 2D Shape, 3D Shape and Angles Data & Chance

Lesson 71 · Constructing Triangles from Given Measurements

Download Activity Book page (PDF)

End of lesson

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~11 mins

3 - Try It Together ~8 mins

Build a triangle from three sides

4 - Construct the Triangle in Your Copy ~6 mins

5 - Class Challenge ~11 mins

Build four triangles from given sides

6 - What Did We Notice? ~6 mins

7 - What's Next ~4 mins

Key Takeaways

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