KS 3 Mathematics S 6 Constructing Triangles 1

KS 3 Mathematics S 6 Constructing Triangles 1 of 51 © Boardworks Ltd 2004

Constructing a triangle given SAS How could we construct a triangle given the lengths of two of its sides and the angle between them? side angle side The angle between the two sides is often called the included angle. We use the abbreviation SAS to stand for Side, Angle and Side. 2 of 51 © Boardworks Ltd 2004

Constructing a triangle given SAS For example, construct and BC = 5 cm. ABC with AB = 6 cm, Start by drawing side AB with a ruler. C 5 cm Use a protractor to mark an angle of 68° from point B. Use a ruler to draw a line of 5 cm from B to C. B = 68° A 6 cm B Join A to C using a ruler to complete the triangle. 3 of 51 © Boardworks Ltd 2004

Constructing a triangle given ASA How could we construct a triangle given two angles and the length of the side between them? angle side The side between the two angles is often called the included side. We use the abbreviation ASA to stand for Angle, Side and Angle. 4 of 51 © Boardworks Ltd 2004

Constructing a triangle given ASA For example, construct and B = 115°. ABC with AB = 10 cm, A = 35° C Start by drawing side AB with a ruler. Use a protractor to mark an angle of 35° from point A. Use a ruler to draw a long line from A. Use a protractor to mark an angle of 115° from point B. 35° A 10 cm 115° B Use a ruler to draw a line from B to meet the other line at point C. 5 of 51 © Boardworks Ltd 2004

Constructing a triangle given SSS How could we construct a triangle given the lengths of three sides? side Hint: We would need to use a compass. We use the abbreviation SSS to stand for Side, Side. 6 of 51 © Boardworks Ltd 2004

Constructing a triangle given SSS For example, construct ABC with AB = 4 cm, BC = 3 cm and AC = 5 cm. C Start by drawing side AB with a ruler. Use a compass and stretch 5 cm it out to a length of 5 cm. 3 cm Put the point of the compass at point A and draw an arc above A 4 cm B line AB. Next, stretch the compass out to a length of 3 cm. Put the point of the compass at point B and draw an arc crossing over the other one. This is point C. Draw lines AC and BC to complete the triangle. 7 of 51 © Boardworks Ltd 2004

Constructing a triangle given RHS Remember, the longest side in a right-angled triangle is called the hypotenuse. How could we construct a right-angled triangle given the right angle, the length of the hypotenuse and the length of one other side? hypotenuse right angle side We use the abbreviation RHS to stand for Right angle, Hypotenuse and Side. 8 of 51 © Boardworks Ltd 2004

Constructing a triangle given RHS For example, construct and AC = 7 cm. ABC with AB = 5 cm, C Start by drawing side AB with a ruler. Extend AB and use a compass to construct a perpendicular at point B. Open the compass to 7 cm. B = 90° 7 cm A 5 cm B Place the point of the compass on A and draw an arc on the perpendicular. Label this point C and complete the triangle. 9 of 51 © Boardworks Ltd 2004