Triangle construction from data

Build from data, then check

For a triangle with sides 5 cm, 6 cm and 7 cm, draw a 7 cm base AB. Draw an arc of radius 5 cm centred on A and one of radius 6 cm centred on B. Their intersection C gives AC = 5 cm and BC = 6 cm. Join the sides and check all three lengths. The reflected intersection on the other side of AB makes a congruent triangle.

Before constructing, check possibility: lengths 2 cm, 3 cm and 6 cm cannot close into a triangle because 2 + 3 is less than 6. A failed compass intersection can signal impossible data rather than poor drawing.

A side and two angles give another construction

For AB = 6 cm, angle CAB = 50° and angle CBA = 65°, draw AB. At A construct a 50° ray on the chosen side; at B construct a 65° ray on that same side. Their intersection is C. The remaining angle is 65°, checking the triangle angle sum.

Specify which side of the base contains the vertex when orientation matters. A reflected construction can have the same lengths and angles without occupying the same position on the page.

Check your understanding 1 Check possibility before using instruments

Can sides 4 cm, 5 cm and 10 cm form a triangle? What happens when the two shorter lengths sum exactly to the longest?

Your answer or drawing on paper

Show answer

No: 4 + 5 < 10, so the sides cannot close. Equality gives a degenerate straight arrangement rather than a non-degenerate triangle. A correct construction needs strict triangle inequalities.

Verification has a physical part

Measure all specified sides and angles on the drawing and explain which construction step established each. A typed numerical response cannot certify the accuracy of a paper compass or protractor construction.