2. Polygons
A gift-shop owner sees the eight-sided sign she ordered from the local sign maker and says, “You got it
wrong. I wanted an octagon like a stop sign.”
Do you think the sign maker or the gift-shop owner was to blame for the wrong sign? Explain.
If you ordered a sign for a shop, what would you do to make sure you received the correct sign?
4. Definition of a Polygon
Closed figure
Straight sides
No curves
No overlapping
5. Types of Polygons
POLYGON DESCRIPTION DRAWING
Triangle 3-sided figure, sum of interior
angles is 180°
Quadrilateral 4-sided figure, sum of interior
angles is 360°
Pentagon 5-sided figure, sum of interior
angles is 540°
Hexagon 6-sided figure, sum of interior
angles is 720°
Octagon 8-sided figure, sum of interior
angles is 1080°
6. Classification of Quadrilaterals
QUADRILATERAL SPECIFIC PROPERTIES DRAWING
Trapezoid Only one set of parallel sides
Parallelogram 2 sets of parallel sides, 2 sets of
congruent sides, opposite angles
congruent
Rectangle All properties of the parallelogram
and 4 right angles
Rhombus ALL properties of the parallelogram
and 4 congruent sides (a slanted
square)
Square ALL properties of the parallelogram
AND the rectangle AND the
rhombus (most specific member of
the quadrilaterals)
7. Freehand Drawing
You can draw geometric figures freehand.
How would you draw a rectangle?
You know that a rectangle has 2 pairs of parallel segments and each pair has the same length.
Draw the first pair of parallel segments of equal length and the same distance apart.
To indicate that your segments are parallel, you can draw arrows on them.
You also know that each corner of a rectangle is a right angle.
Draw the second pair of segments perpendicular to the first pair.
To indicate right angles, draw a small box in each corner.
Finally, to indicate that the two shorter segments are parallel, you can draw double arrows on them.
**Freehand drawings are meant to show the general shape of a figure.
The measurements might not be exact.**
8. Draw a quadrilateral for each given description:
Exactly one pair of perpendicular sides.
Two pairs of parallel sides and no right angles.
A quadrilateral with exactly one pair of parallel sides.
9. Geometric Tools Drawing
You can draw more precise geometric figures with a ruler and protractor.
Draw a parallelogram with two 3-in. sides, two 4-in. sides, two 60° angles, and two 120° angles.
To draw a parallelogram, begin by drawing one of its sides. Use the ruler to measure and draw a 4-in
segment. Label the length.
Next, measure an angle so you can draw a connecting side. Center the protractor on one endpoint of the
segment and align the segment with the zero on the protractor.
Find 60° on the scale that starts with zero and make a mark to show the measurement. Align the ruler to
connect the endpoint with the mark. Then use the ruler to measure a 3-in segment.
10. Geometric Tools Drawing
Draw a parallelogram with two 3-in. sides, two 4-in. sides, two 60° angles, and two 120° angles.
Draw another 3-in segment parallel to the first 3-in segment. Use the endpoint of the base segment to start the new segment.
Center the protractor on the endpoint and align the segment with the zero on the protractor. Find 120° on the scale and make a mark to show the measurement. Align the
ruler to connect the endpoint with the mark.
Then use the ruler to measure a 3-in segment. Use the ruler to draw and measure the top segment of the parallelogram.
The opposite angles of a parallelogram are equal.
Use arrows to show that the pairs of lines are parallel.
11. Sketching Figures
Use the ruler and protractor to sketch the figure. If the figure is not possible, explain why.
A rectangle with two sides 4-in. and two sides 2-in.
A triangle with two 100° angles.
A figure with two sides 1-in., two sides 3-in., and at least one right angle.
12. Draw the following figures.
A square with side lengths of 10 inches.
A quadrilateral with one angle measure of 50° and one side length of 4 inches.
Draw a rhombus with side lengths of 4 inches and angle measures of 40°, 140°, 40°, and 140°.
13. Sketching and Describing
What geometric shapes can you draw that have exactly two pairs of perpendicular sides?
Trapezoid and Kite
What geometric shapes can you draw that have no pairs of parallel sides?
Regular Pentagon
What quadrilaterals can you draw that have four sides with length 3 centimeters?
Square and Rhombus
14. Sketching and Describing
Sketch a four-sided sandbox that has more than two right angles, two side lengths 5 centimeters, and two side lengths 6 centimeters.
What geometric shape best describes the shape of the sandbox?
Rectangle
A friend is building a garden with two side lengths 4 centimeters and exactly one right angle. What geometric figures could describe
how the garden might look?
Quadrilateral, Kite, and Isosceles right triangle
Sketch a pond shaped like a quadrilateral with side lengths 3 inches and no right angles. What geometric shape best describes the
shape of the pond?
Rhombus
15. Sketching and Describing
Draw a rectangle with the given conditions: two sides with a length of 3.5 centimeters and two sides with a
length of 5 centimeters.
Draw a kite that has one right angle with side lengths 4 inches and 7 inches. The perpendicular sides of the kite
are of length 4 inches.
Draw a quadrilateral with one angle measure of 60° and exactly one side length of 3 centimeters.
