KS3 Mathematics

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# KS3 Mathematics - PowerPoint PPT Presentation

KS3 Mathematics. S6 Constructing Triangles. 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 .

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### KS3 Mathematics

S6 Constructing Triangles

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°

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.

Place the point of the compass on A and draw an arc on the perpendicular.

Label this point C and complete the triangle.