Warm-Up Exercises

1. Draw an acute angle and shade the interior.

2. Find the measure of the supplement of a 130º angle.

ANSWER

ANSWER 50

3. Find the measure of the complement of an 86 angle.

ANSWER 4

Warm-Up Exercises

Warm-Up Exercises 1.6 Classify Polygons Goal: Classify polygons. Key Vocabulary: •  polygon •  sides of a polygon •  vertex of a polygon •  convex polygon •  concave polygon •  n-gon •  equilateral polygon •  equiangular polygon •  regular polygon

Warm-Up Exercises 1.6 Classify Polygons

Goal: Classify polygons.

Postulates, Corollaries, and Theorems: •  None

Warm-Up Exercises Definitions POLYGON: A closed figure with the following properties: 1)  It is formed by three or more line segments

called sides 2)  Each side intersects exactly two sides, one at

each endpoint, so that no two sides with a common endpoint are collinear.

Warm-Up Exercises Definitions POLYGON: Each endpoint of a side is a vertex of the polygon. The plural of vertex is vertices. A polygon can be named by listing the vertices in consecutive order. For example, ABCDE and CDEAB are both correct names for the polygon below.

Warm-Up Exercises Definitions CONVEX POLYGON: A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. A polygon that is not convex is nonconvex or concave.

Warm-Up Exercises Definitions CONCAVE POLYGON: A polygon that is not convex. Tip: Concave figures have segments that go inward, like an entrance to a cave.

Warm-Up Exercises Definitions n-GON: A polygon with n sides.

A triangle is also a 3-gon. A 14 sided polygon is a 14-gon.

Warm-Up Exercises Definitions EQUILATERAL POLYGON: A polygon with all of its sides congruent.

Warm-Up Exercises Definitions EQUIANGULAR POLYGON: A polygon with all of its interior angles congruent.

Warm-Up Exercises Definitions REGULAR POLYGON: A polygon that has all sides and all angles congruent.

Warm-Up Exercises EXAMPLE 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 Exercises EXAMPLE 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 Exercises EXAMPLE 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 Exercises GUIDED PRACTICE for Examples 1 and 2

Sketch an example of a convex pentagon and an example of a concave decagon.

1.

ANSWER

Warm-Up Exercises GUIDED 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 Exercises EXAMPLE 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 – 2 8 = 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 Exercises EXAMPLE 3 Find side lengths

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

30 3(8) + 6 = = 3x + 6

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

ANSWER

Warm-Up Exercises GUIDED 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.

120o ANSWER

Warm-Up Exercises Daily Homework Quiz

1. Draw a convex hexagon.

ANSWER

quadrilaterals ; not regular ANSWER

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

Warm-Up Exercises Daily Homework Quiz

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

ANSWER 16

Warm-Up Exercises Closing •  A polygon is a plane figure formed by three or more line segments. Each side intersects exactly two other sides, on at each endpoint, so that no two 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 sides are congruent and all angles in the interior are congruent.

Warm-Up Exercises Closing 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 or 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.

Warm-Up Exercises 1.6 Homework

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