1.6 Classify Polygons

• You will classify polygons

• Essential Question: How do you classify polygons?

Warm-Up Exercises

Some things may be different than they appear!!

Assume!• Lines are straight• If two lines intersect, they

intersect at one point• Points on a line are collinear• All points in a diagram are

coplanar unless planes are drawn to show they are not coplanar

Do NOT assume!• Two lines are parallel

because they LOOK parallel (They MUST be marked)

• Two lines are perpendicular because they look perpendicular (they MUST be marked)

• Pairs of angles, segments, or polygons are congruent (they MUST be marked)

Warm-Up ExercisesEXAMPLE 1 Identify polygons

SOLUTION

Tell whether the figure is a polygon and whether it is convex or concave.

Some segments intersect more than two segments, so it is not a polygon.

a.

b. The figure is a convex polygon.

d. The figure is a concave polygon.

Part of the figure is not a segment, so it is not a polygon.

c.

b. c.a. d.

Warm-Up ExercisesEXAMPLE 2 Classify polygons

SOLUTION

Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning.a. b.

The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon.

a.

The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular.

b.

Warm-Up ExercisesEXAMPLE 2 Classify polygons

c. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so it is equilateral. The polygon is not convex, so it is not regular.

Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning.

c.

SOLUTION

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Sketch an example of a convex heptagon and an example of a concave heptagon.

1.

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2

Classify the polygon shown at the right by the number of sides. Explain how you know that the sides of the polygon are congruent and that the angles of the polygon are congruent.

2.

Quadrilateral. They all have the same measure; they are all right angles.

ANSWER

Warm-Up ExercisesEXAMPLE 3 Find side lengths

SOLUTION

First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent.

Write equation.

Subtract 3x from each side.Add 2 to each side.

3x + 6 4x – 2=6 = x – 28 = x

A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side.

ALGEBRA

Warm-Up ExercisesEXAMPLE 3 Find side lengths

Then find a side length. Evaluate one of the expressions when x = 8.

303(8) + 6 ==3x + 6

The length of a side of the table is 30 inches.

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

The expressions 8y° and ( 9y – 15 )° represent the measures of two of the angles in the table in Example 3. Find the measure of an angle.

3.

120oANSWER

Warm-Up ExercisesDaily Homework Quiz

1. Draw a convex hexagon.

ANSWER

quadrilaterals ; not regularANSWER

2. This figure shows the tiles on a kitchen floor. What type of polygon are the tiles? Are they regular polygons?

Warm-Up ExercisesDaily Homework Quiz

3. This figure is a regular polygon. Find the length of each side.

ANSWER 16

Scavenger HuntName Description/Definition Image (Real world example)

Triangle Sides: 3A triangle is a 3 sided figure that has three interior angles that add up to 180o and the sides are straight lines.

• You will classify polygons

• Essential Question: How do you classify polygons?• A polygon is a plane figure

formed by 3 or more line segments. Each side intersects exactly 2 other sides, one at each endpoint, so that no 2 sides with a common endpoint are collinear.• A polygon is convex if no line

that contains a side of the polygon contains a point in the interior. Otherwise, the polygon is concave.• A polygon is regular if all sidea

re congruent and all angles in the interior are congruent.

The most basic way of classifying a polygon is by the number of sides. You can also tell whether the polygon is convex or concave, or indicate whether all the sides of angles are congruent. If all the sides of a convex polygon are congruent and all the angles are congruent, the polygon is a regular polygon.