# Geometry Quiz: How well do you know geometry?

Below you will find 5 geometry questions that will test how well you know the subject.  Enjoy yourself as you take on the challenge.

### Geometry Quiz

1.Using the figure below, find lengths $$BC$$ and $$BD$$.

2. For the following figure, find angles $$a,b$$ and $$c$$.

3. Find the sums of angles $$\angle A+\angle C$$ for the following figure.

4. For the figure below, find the length $$AF$$.

5. Suppose that a line segment with left endpoint $$A$$ and right endpoint $$B$$ has length 6 inches.  Choose a point $$P$$ on the line segment $$\overline{AB}$$.  You then construct a right triangle so that both legs have length $$AP$$ and a square that has side length $$PB$$ (see figure below, not to scale).  How far from $$A$$ should you place $$P$$ in order to minimize the sum of the areas of the triangle and the square?

### Submission

Submit your answers in the form below to be taken to the solutions page.  Here you can see how well you did!

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