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State True or False in each of the following statements.
There is a diagram of a triangle $$ABC$$ right angled at $$A$$ and the perpendicular drawn from $$A$$ onto the side $$BC$$ is meeting the side $$BC$$ in $$D$$. There are exactly two similar triangles in the diagram.
Correct Answer: False
The diagram contains three triangles, $$ABC$$, $$DBA$$ and $$DAC$$. Each of $$DBA$$ and $$DAC$$ shares an acute angle with $$ABC$$ and has a right angle, so all three are similar to one another, $$\triangle ABC \sim \triangle DBA \sim \triangle DAC$$. There are three similar triangles, not exactly two, so the statement is False.
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