The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Constructing triangles – worksheets to print
Construct triangles from three given parts and measure them, name the matching congruence rule (SSS, SAS, ASA, SSA) and decide whether the triangle exists at all (triangle inequality, angle sum).
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Constructing triangles: explained simply
Three suitable parts fix a triangle completely. The congruence rules tell you which parts are enough. You construct with a ruler, compasses and a set square.
How to work it out
- SSS: three sides. SAS: two sides and the angle between them.
- ASA: one side and the two angles at its ends.
- SSA: two sides and the angle opposite the longer side.
- Triangle inequality: any two sides together are longer than the third. Angle sum: α + β + γ = 180°.
An example, step by step
Construct the triangle ABC with c = 6 cm, α = 50° and β = 60° (ASA).
- Draw the line segment AB = 6 cm.
- Draw the angle α = 50° at A and the angle β = 60° at B.
- C is where the two free arms meet. γ = 180° − 50° − 60° = 70°.
Understand other variations
Three sides (SSS)
a = 4 cm, b = 5 cm, c = 6 cm: draw AB = 6 cm, draw a circle of 5 cm around A and one of 4 cm around B. Where they cross is C.
Does the triangle exist?
3 cm, 4 cm and 8 cm: 3 + 4 = 7 is less than 8 – no triangle. α = 100° and β = 90° already add up to more than 180°.
Not unique
Three angles only fix the shape, not the size. If the angle is opposite the shorter side, there can be two different triangles.
Your turn
Is there a triangle with a = 5 cm, b = 6 cm and c = 12 cm?
Show the answer and method
No: 5 + 6 = 11 is less than 12.
Ready-made worksheets: Constructing triangles
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