Revision:Similar Triangles

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Similar Triangles

If two shapes are similar, one is an enlargement of the other. This means that the two shapes will have the same angles and their sides will be in the same proportion (e.g. the sides of one triangle will all be 3 times the sides of the other etc.).

(diagram of similar triangles missing)

angle A = angle D angle B = angle E angle C = angle F

Two triangles are similar if:

1. 3 angles of 1 triangle are the same as 3 angles of the other or
2. 3 pairs of corresponding sides are in the same ratio or
3. An angle of 1 triangle is the same as the angle of the other triangle and the sides containing these angles are in the same ratio.

Example

In the above diagram, the triangles are similar. EF = 6cm and BC = 2cm . What is the length of DE if AB is 3cm? EF = 3BC, so DE = 3AB = 9cm.

Comments

The example above is rather basic and doesn't show the full level of knowledge that is required from this topic - eg a question involving basic algebra (even if the method is the same, the algebra makes the question trickier). Also the question works forwards with a whole number scale factor - more difficult questions involve working out the smaller length. Questions could also involve pythag or trig and proving two triangles are similar form a limited amount of info about them - this ought to be covered by the article.

The article also focuses on triangles. Questions will most likely be about triangles, but also on other shapes.

No mention of area is made either - a reminder that scale factors for areas etc, differ from scale factors for lengths should be added as a reminder.