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Constructing Triangles Worksheet

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Constructing Triangles Worksheet

A design team is making triangular frames. Use triangle facts and accurate ruler, compass and protractor methods to check which frames can be built. Show working where asked. For drawing tasks, use a ruler and the stated measurements.

Check the Design

A unique triangle can be constructed from three side lengths (SSS), two sides and their included angle (SAS), or two angles and a corresponding side (ASA/AAS). The three angles alone do not fix the triangle’s size.

1.The frame plan gives side lengths 5 cm, 7 cm and 9 cm. Which construction information is this, and is it enough to determine one triangle?

2.A second plan gives sides 6 cm and 8 cm with the included angle of 45°. What does SAS mean, and can this information determine a unique triangle?

3.Which set of information is not enough to determine a unique triangle?

Three side lengths: 4 cm, 5 cm and 6 cm
Two sides: 6 cm and 8 cm, with their included angle 45°
Three angles: 50°, 60° and 70°
Two angles: 40° and 80°, with the side between them 7 cm

4.A frame is planned with sides 3 cm, 4 cm and 10 cm. Explain why it cannot form a triangle.

5.Decide whether lengths 4 cm, 6 cm and 9 cm can make a triangle. Check the triangle inequality by adding the two shortest lengths and state your decision.

Plan a Precise Construction

For an SSS construction, draw one side first. Set the compass to each of the other two side lengths and draw arcs from the endpoints of the base. Their intersection is the third vertex. Join the vertices and leave the arcs visible as construction marks.

6.For triangle ABC, AB = 7 cm, BC = 5 cm and AC = 6 cm. Which side could you choose as the base? Give one sensible choice and explain why there is no required longest-side rule.

7.After drawing AB = 7 cm for the SSS construction in question 6, describe how to locate C using a compass.

8.For triangle PQR, PQ = 8 cm, angle P = 50° and PR = 6 cm. Write a clear ruler-and-protractor construction plan, in order.

Build and Check

Use a ruler, compass and protractor for the constructions below. Keep your arcs visible and label each vertex and measurement.

9.Construct triangle ABC with AB = 8 cm, BC = 6 cm and CA = 7 cm. Show your compass arcs and label all three side lengths.

10.For the triangle you constructed in question 9, estimate or measure angles A, B and C with a protractor. Check that their total is 180°. (Measurements may differ slightly because of drawing accuracy.)

11.Construct triangle DEF with DE = 9 cm, angle D = 60° and DF = 5 cm. Label the known measurements and show the angle construction marks.

12.A teammate says, “If I know all three angles of a triangle, I can construct exactly one triangle.” Explain what is wrong with this claim.