# Problem of the Week Problem B and Solution Draw Me!

## Problem

Using a protractor and a ruler, follow the instructions below to draw three different shapes.

1. Steps for drawing Shape $$1$$:

• Draw a horizontal line segment $$AB$$ of length $$4\,$$cm.

• From $$B$$, draw line segment $$BC$$ of length $$8\,$$cm at an angle of $$32\degree$$ to $$AB$$.

• Draw a line segment connecting $$C$$ and $$A$$.

What is the measure of angle $$ACB$$ in your shape?

What kind of triangle did you draw?

2. Steps for drawing Shape $$2$$:

• Draw a horizontal line segment $$AB$$ of length $$6\,$$cm.

• From $$B$$, draw line segment $$BC$$ of length $$7\,$$cm at an angle of $$135\degree$$ to $$AB$$.

• From $$C$$, draw line segment $$CD$$ of length $$6\,$$cm at an angle of $$45\degree$$ to $$BC$$, parallel to $$AB$$.

• Draw a line segment connecting $$D$$ and $$A$$.

What shape did you draw?

3. Steps for drawing Shape $$3$$:

• Draw a vertical line segment $$AB$$ of length $$5\,$$cm.

• From $$B$$, draw line segment $$BC$$ of length $$5\,$$cm at an angle of $$90\degree$$ to $$AB$$.

• Draw line segment $$AD$$ of length $$7\,$$cm, parallel to $$BC$$.

• Draw a line segment connecting $$D$$ and $$C$$.

What shape did you draw?

## Solution

1. Following the steps for Shape 1 creates a scalene triangle. The measure of angle $$ACB$$ is $$25\degree$$.

2. Following the steps for Shape 2 creates a parallelogram, which is a quadrilateral with two pairs of parallel sides.

3. Following the steps for Shape 3 creates a right trapezoid, which is a quadrilateral with one pair of parallel sides and two right angles.