S6 Constructing Triangles

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KS3 Mathematics

• S6 Constructing Triangles

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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.
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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.
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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.
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Constructing a triangle given ASA
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
B
10 cm
Use a ruler to draw a line from B to meet the
other line at point C.
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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.
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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
B
4 cm
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.
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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.
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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.