Constructing Triangles Grade 6 Geometry The aim of this unit is to teach pupils to: Construct lines, angles and shapes Find simple loci, both by reasoning and by using ICT Material in this unit is linked to the Key Stage 3 Framework supplement of examples pp 220-227. Constructing Triangles

Re-cap What is an isosceles, scalene, and equilateral triangle? What is an acute, obtuse and right triangle?

Mind-On.... Construct the following: - Right triangle Acute triangle Scalene triangle

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.

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

Constructing a triangle given ASA How could we construct a triangle given two angles and the length of the side between them? angle 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.

Constructing a triangle given ASA For example, construct ABC with AB = 10 cm, A = 35° and B = 115°. 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. 115° 35° Ask pupils how we could check that this triangle has been constructed correctly. Establish that we could measure angle C to verify that it measures 30°. Remind pupils that construction lines should not be rubbed out. Use a protractor to mark an angle of 115° from point B. A 10 cm B Use a ruler to draw a line from B to meet the other line at point C.

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

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 it out to a length of 5 cm. 5 cm 3 cm Put the point of the compass at point A and draw an arc above line AB. A 4 cm B 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.

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.

Constructing a triangle given RHS For example, construct ABC with AB = 5 cm, B = 90° and AC = 7 cm. C Start by drawing side AB with a ruler. 7 cm Extend AB and use a compass to construct a perpendicular at point B. A 5 cm B Open the compass to 7 cm. Ask pupils how we know that, if angle B is a right-angle, side AC must be the hypotenuse. The hypotenuse, the longest side in a right-angled triangle, must always be the side opposite the right angle. Review the construction of a perpendicular from a point on a line on slide 24. Place the point of the compass on A and draw an arc on the perpendicular. Label this point C and complete the triangle.