# 1.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Classify...

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### Transcript of 1.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Classify...

Slide 11. 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

1.6

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.

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.

1.6

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.

1.6

SOLUTION

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

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.

c.

1.6

Guided Practice

SAMPLE ANSWER

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

1.

1.6

Guided Practice

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

1.6

Example 4

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

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.

3x + 6

4x – 2

Example 4

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

SOLUTION

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

3(8) + 6

30 inches.

Guided Practice

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

1.6

ANSWER

ANSWER

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

1.6

Lesson Quiz

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

ANSWER

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

1.6

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.

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.

1.6

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.

1.6

SOLUTION

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

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.

c.

1.6

Guided Practice

SAMPLE ANSWER

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

1.

1.6

Guided Practice

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

1.6

Example 4

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

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.

3x + 6

4x – 2

Example 4

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

SOLUTION

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

3(8) + 6

30 inches.

Guided Practice

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

1.6

ANSWER

ANSWER

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

1.6

Lesson Quiz

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

ANSWER

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