1. Constructing Triangles Objective: to construct different types of triangles. Starter – work out the missing angles in the following triangles: A B C

2. Equipment needed for constructions Before you begin make sure you have the following equipment: A protractor A ruler marked in cm and mm A compass A sharp pencil

3. Constructing triangles To accurately construct a triangle you need to know: The length of two sides and the included angle (SAS) The size of two angles and a side (ASA) The lengths of three of the sides (SSS) Or A right angle, the length of the hypotenuse and the length of one other side (RHS)

4. Constructing SAS Triangles How could we construct a triangle given the lengths of two of its sides and the angle between them? The angle between the two sides is often called the included angle. side angle Side Angle Side

5. Constructing SAS Triangles For example, construct triangle ABC with AB = 6 cm, B = 68° and BC = 5 cm. Step 1: Start by drawing side AB with a ruler. Step 2: Use a protractor to mark an angle of 68° from point B. A6 cmB C 5 cm 68° Step 3: Use a ruler to draw a line of 5 cm from B to C. Step 4: Join A to C using a ruler to complete the triangle.

6. Constructing ASA Triangles How could we construct a triangle given two angles and the length of the side between them? The side between the two angles is often called the included side. Angle Side Angle side angle

7. Constructing ASA Triangles For example, construct triangle ABC with AB = 10 cm, A = 35° and B = 155°. Step 1: Start by drawing side AB with a ruler. Step 2: Use a protractor to mark an angle of 35° from point A. Step 3: Use a ruler to draw a long line from A. Step 4: Use a protractor to mark an angle of 115° from point B. Step 5: Use a ruler to draw a line from B to meet the other line at point C. AB10 cm C 35° 115°

8. Constructing SSS Triangles How could we construct a triangle given the lengths of three sides? To construct this angle you will need to use a compass. Side Side Side side

9. Constructing SSS Triangles For example, construct triangle ABC with AB = 4cm, BC = 3cm and AC = 5cm. Step 1: Start by drawing side AB with a ruler. Step 2: Open a pair of compasses to a length of 5cm. Step 3: Put the compass needle at point A and draw an arc above line AB. Step 4: Next, open the compasses out to a length of 3cm. Step 5: Put the compass needle at point B and draw an arc crossing over the other one. This is point C. Step 6: Draw lines AC and BC to complete the triangle. AB4 cm C 3 cm 5 cm

10. Constructing RHS Triangles How could we construct a right-angled triangle given the right angle, the length of the hypotenuse and the length of one other side? Remember, the longest side in a right-angled triangle is called the hypotenuse. Right angle Hypotenuse Side hypotenuse right angle side

11. Constructing RHS Triangles For example, construct triangle ABC with AB = 5cm, BC = 90° and AC = 7cm. Step 1: Start by drawing side AB with a ruler. Step 2: Extend AB and use compasses to construct a perpendicular at point B. Step 3: Open the compasses to 7cm. Step 4: Place the compass needle on A and draw an arc on the perpendicular. Step 5: Label this point C and complete the triangle. A5 cmB C 7 cm

12. Task Complete the worksheet.worksheet