Lesson 11.1 Name Polygons Measurement and Data—
Name
Polygons
Essential Question How can you identify and classify polygons?
UUnnlloocckk tthhee PPrroobblleemm
The Castel del Monte in Apulia, Italy, was built more than 750 years ago. The fortress has one central building with eight surrounding towers. Which polygon do you see repeated in the structure? How many sides, angles, and vertices does this polygon have?
A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. It is named by the number of sides and angles it has. To identify the repeated polygon in the fortress, complete the tables below.
Lesson 11.1
Measurement and Data-- 5.G.B.3, 5.G.B.4 MATHEMATICAL PRACTICES MP5, MP7, MP8
? Houghton Mifflin Harcourt Publishing Company ? Image Credits: (tr) ?De Agostini/Getty Images
Polygon Sides Angles
Vertices
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon
Sometimes the angles inside a polygon are greater than 180?.
Polygon Sides Angles
Vertices
Heptagon 7
Octagon 8
Nonagon
Decagon
So, the __ is the repeated polygon in the Castel del Monte because it has _ sides, _ angles, and _ vertices.
275
MTaatlkh
MATHEMATICAL PRACTICES 5
Use Patterns What pattern do you see among the number of sides, angles, and vertices a polygon has?
Chapter 11 637
Regular Polygons When line segments have the same length
or when angles have the same measure, they are congruent. Two polygons are congruent when they have the same size and the same shape. In a regular polygon, all sides are congruent and all angles are congruent.
regular polygon
not a regular polygon
All sides are congruent.
4 cm 108? 4 cm
108?
108?
All angles 4 cm
4 cm
108? 108?
are congruent.
4 cm
You can write measurements to show congruent sides and angles.
Not all sides are congruent.
Not all angles are congruent.
You can use the same markings to show the congruent sides and angles.
Try This! Label the Venn diagram to classify the polygons in each group.
Then draw a polygon that belongs only to each group.
Congruent ___
Congruent ___
? Houghton Mifflin Harcourt Publishing Company
Regular ___
SShhaarree aanndd SShhooww
MATH
BOARD
1. Name the polygon. Then use the markings on the figure to tell whether it is a regular polygon or not a regular polygon.
MTaatlkh
MATHEMATICAL PRACTICES 1
Describe Relationships Explain how the group of polygons in the center section of the Venn diagram is related to the groups in the left and right sections of the diagram.
a. Name the polygon. ___
b. Are all the sides and all the angles congruent? ___
c. Is the polygon a regular polygon? ___
638
Name
Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.
2.
3.
4.
MTaatlkh
MATHEMATICAL PRACTICES 2
Use Reasoning Why do all regular pentagons have the same shape?
OOnn YYoouurr OOwwnn
Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.
5.
6.
7.
8.
? Houghton Mifflin Harcourt Publishing Company
9.
DEEPER Compare the polygons shown in Exercises 2 and 8.
Describe how they are alike and how they are different.
Chapter 11 ? Lesson 1 639
MATHEMATICAL PRACTICES ANALYZEt-00,'034536$563&t13&$*4*0/
OOqqnnaakkddllRRnnkkuuhhmmff??@@ooookkhhbb``sshhnnmmrr
For 10?11, use the Castel del Monte floor plan at the right.
10. DEEPER Which polygons in the floor plan have four equal sides and four congruent angles? How many of these polygons are there?
11. DEEPER Is there a quadrilateral in the floor plan that is not a regular polygon? Name the quadrilateral and tell how many of the quadrilaterals are in the floor plan.
12.
MATHEMATICAL PRACTICE
6
Use Math Vocabulary Sketch eight points that are
vertices of a closed plane figure. Connect the points to draw the figure.
What kind of polygon did you draw?
13.
SMARTER Look at the angles for all regular polygons. As the
number of sides increases, do the measures of the angles increase or
decrease? What pattern do you see?
14.
SMARTER Kayla drew the shape shown. For 14a?14b, choose
the values and term that correctly describe the shape Kayla drew.
4
4
14a. The figure has 6 sides and 6 angles.
12
8
regular heptagon 14b. The figure is a regular pentagon .
regular hexagon
640
? Houghton Mifflin Harcourt Publishing Company
Name
Polygons
Practice and Homework
Lesson 11.1
Name each polygon. Then tell whether it is a regular polygon or not a regular polygon.
1.
2.
COMMON CORE STANDARD--5.G.B.3 Classify two-dimensional figures into categories based on their properties.
4 sides, 4 vertices, 4 angles means it is a _qu_ adrilater_ al . The sides are not all congruent, so it is _ not_ regula_ r . 3.
______ 4.
______
______
5.
6.
? Houghton Mifflin Harcourt Publishing Company
______
______
PPrroobblleemm SSoollvviinngg
7. Sketch nine points. Then, connect the points to form a closed plane figure. What kind of polygon did you draw?
8. Sketch seven points. Then, connect the points to form a closed plane figure. What kind of polygon did you draw?
______
______
9. WRITE Math Use grid paper to draw one regular hexagon and one
hexagon that is not regular. Explain the difference.
Chapter 11 641
Lesson Check (5.G.B.3)
1. Name the polygon. Write whether it is regular or not regular.
2. Name the polygon. Write whether it is regular or not regular.
Spiral Review (5.OA.A.2, 5.NBT.B.7, 5.MD.A.1)
3. Ann needs 42 feet of fabric to make a small quilt. How many yards of fabric should she buy?
4. Todd begins piano practice at 4:15 p.m. and ends at 5:50 p.m. How long does he practice?
? Houghton Mifflin Harcourt Publishing Company
5. Jenna has 30 barrettes. She is organizing her barrettes into 6 boxes. She puts the same number of barrettes in each box. Write an expression that you can use to find the number of barrettes in each box.
6. Melody had $45. She spent $32.75 on a blouse. Then her mother gave her $15.50. How much money does Melody have now?
642
FOR MORE PRACTICE GO TO THE
Personal Math Trainer
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.