Explain how we can show that triangle ABC and triangle CDE are similar.
C D Solution E
A
B
Corresponding sides
The corresponding sides face the corresponding angles, as shown in the diagram on the right. For example, the sides that face the angles with two arcs are corresponding, and are shown in blue.
Worked example 2
Show that the triangles shown are similar and identify the corresponding sides.
K L Solution M G H F
Discuss and discover Work with a classmate to complete the steps below.
(i) Construct a triangle ABC with side lengths |AB| = 6 cm, |BC| = 5 cm and |AC| = 4 cm.
(ii) Construct another triangle XYZ with side lengths |XY| = 12 cm, |XZ| = 10 cm and |YZ| = 8 cm. (iii) What is the relationship between the lengths of the sides of these two triangles? (iv) Use a protractor to measure the angles in each of the triangles. (v) What do you notice?
(vi) How would you describe these two triangles? Give a reason for your answer. (vii) List the corresponding sides in these two triangles. (viii) Investigate if