year 8 maths

512 Chapter 8 Transformations and congruence
Investigating congruence with dynamic geometry software
Computer dynamic geometry is ideal for these activities but geometrical instruments could also be used.
Investigation
Conditions for congruent triangles
1 SSS
a Construct a triangle with side lengths 4 cm , 7 cm and 9 cm . Measure the given side lengths using
one decimal place, and if using dynamic geometry adjust the triangle to suit. Use the measure tool
for the side lengths.
b Construct a second triangle with the same side lengths.
c Do your two triangles look congruent? Measure the angles to help check.
d Can you draw another triangle given the same information so that it does not look congruent to
the others?
4.0 cm
9.0 cm
7.0 cm
4.0 cm
9.0 cm
7.0 cm
2 SAS
a Construct a triangle with side lengths 4 cm and 7 cm and an included angle of 30° . Measure the
given side lengths and the angle using one decimal place, and if using dynamic geometry adjust
the triangle to suit.
b Construct a second triangle with the same side lengths and included angle.
c Do your two triangles look congruent? Measure the missing angle and side lengths to help check.
d Can you draw another triangle given the same information so that it does not look congruent to
the others?
3 AAS
a Construct a triangle with two angles, 30° and 50° , and one side length of 6 cm . Measure the given
side length and the angles using one decimal place, and if using dynamic geometry adjust the
triangle to suit.
b Construct a second triangle with the same side length and angles.
c Do your two triangles look congruent? Measure the missing side length and angle to help check.
d Can you draw another triangle given the same information so that it does not look congruent to
the others?
4 RHS
a Construct a triangle with angles of 90° and 50° , hypotenuse of length 6 cm and other side of length
4 cm . Measure the two given side lengths and the angle using one decimal place, and if using
dynamic geometry adjust the triangle to suit.
b Construct a second triangle with the same two side lengths and angles.
c Do your two triangles look congruent? Measure the missing side length and angles to help check.
d Can you draw another triangle given the same information so that it does not look congruent to
the others?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.