Lesson 4.1 - Polygons
Obj.: • classify polygons by their sides. • classify quadrilaterals by their
attributes. • find the sum of the angle measures in a polygon.
Vocabulary
• Decagon - A polygon with ten sides.
• Dodecagon - A polygon with twelve sides.
• Equiangular polygon - A polygon in which all angles are congruent.
• Equilateral polygon - A polygon in which all sides are congruent.
• Heptagon - A polygon with seven sides.
• Hexagon - A polygon with six sides.
• n-gon - A general term used to represent a polygon with n sides.
• Nonagon - A polygon with nine sides.
• Octagon - A polygon with eight sides.
• Parallelogram - A quadrilateral with both pairs of opposite sides parallel.
• Pentagon - A polygon with five sides.
• Polygon - A closed plane figure that is bounded by three or more line segments.
• Quadrilateral - A polygon with four sides.
• Rectangle - A parallelogram with four right angles.
• Regular polygon - A polygon with all sides and all angles congruent.
• Rhombus - A parallelogram with four congruent sides.
• Right angle - An angle whose measure is 90 degrees.
• Square - A parallelogram with four congruent sides and four right angles.
• Trapezoid - A quadrilateral with exactly one pair of parallel sides.
• Triangle - A polygon with three sides.
***ANGLE MEASURES IN A POLYGON***
The sum of the angle measures of a polygon with n sides is 180°(n - 2).
Example 1
Quadrilateral ABCD is a parallelogram. Find the value of x.
43°
Example 2
Find the sum of the angle measures in a dodecagon.
1,800°
**Practice for Lesson 4.1 pages 101 & 102, 1-16 all**
Lesson 4.2 - INVESTIGATION: Formulas and Literal Equations
Obj.: • solve a literal equation for a specific variable. • find the perimeter of a
polygon. • find the circumference of a circle.
Vocabulary
• Circumference - The distance around a circle.
• Formula - An equation that states a rule for the relationship between two or more
real-word quantities.
• Literal equation - A literal equation is an equation that has more than one
variable.
• Perimeter - The distance around a figure.
EXAMPLE 1
Solve the literal equation
2x + 7y = 12 for y.
EXAMPLE 2
The Pentagon, in Alexandria, Virginia, occupies a ground space that is a regular pentagon with side
walls that are 921 feet in length. Find the perimeter of the Pentagon.
4,605 feet
**Practice for Lesson 4.2 pages 105 & 106, 1-18 all**
Lesson 4.3 - ACTIVITY: Area and Package
Obj.: • create a mathematical model for an efficient package design. • use area
formulas to find the areas of various polygons. • use areas of polygons to
evaluate the efficiency of a package design.
Vocabulary
• Area - The measure of the amount of surface occupied by a figure in square units.
When efficient packaging is designed, many criteria are examined.
The packaging must be economical. Conservation of both space and
materials must be considered. Go to pages 107-109 of the textbook.
Now it is your turn to design your own soft-drink package.
Answer questions 1- 6 in the space below.
1. Use handout 4A.
5. a.____________________________
2. ____________________________
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b,____________________________
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3. a.__________________________
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6. a.____________________________
b.__________________________
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b.____________________________
b.__________________________
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c.____________________________
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d.____________________________
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**Practice for Lesson 4.3 pages 109 - 111, 1-14 all**
Lesson 4.4 - INVESTIGATION: Volumes of Solid Figures
Obj.: • use formulas to find the volumes of right prisms, cylinders, cones,
pyramids, and spheres. • use volumes of solids to evaluate the efficiency of a
package design.
Vocabulary
• Cone - A solid with a circular base and a vertex that is not in the same plane as the
base.
• Cube - A solid with six congruent square faces.
• Cylinder - A solid with two congruent circular bases that lie in parallel planes.
• Edges of a solid - The line segment formed by the intersection of two faces of a
solid.
• Faces of a solid - A flat surface of a geometric solid.
• Pyramid - A solid with a polygonal base and lateral faces that are triangles that
have a common vertex.
• Rectangular solid - A solid figure that has six rectangular faces.
• Right prism - A prism in which the lateral edges are perpendicular to both bases.
• Solid - A three-dimensional figure that encloses a portion of space.
• Sphere - The set of all points in space that are equidistant from a given point called
the center.
• Vertices of a solid - The endpoints of the edges of the solid.
• Volume - The amount of space that a three-dimensional object occupies in cubic
units.
In this lesson, you will examine three-dimensional models and use
their volumes to determine the efficiencies of packages. Go to pages
112 & 113 of the textbook.
Answer questions 1- 5 in the space below.
1. ______________________________
4. _____________________________
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2. ______________________________
5. a.____________________________
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3. ______________________________
b.____________________________
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**Practice for Lesson 4.4 pages 114 - 116, 1-20 all**
Lesson 4.5 - Review And Practice
Obj.: • solve problems that require previously learned concepts and skills.
Example 1
Terms whose variable parts are exactly the same are called ___________________________ terms.
Example 2
Choose the correct answer.
Which figure is not a polygon?
A. An equilateral triangle
B. A square
C. A circle
D. A rhombus
Example 3
Multiply or divide.
a. 14.2 X 0.4
b. 0.696 ÷ 5.8
Example 4
Add, subtract, multiply or divide.
a. 0.8 + (‒0.3)
b. ‒8 ÷ (–0.4)
Example 5
Solve.
a. What is 5% of 34?
b. What is 0.5% of 18?
Example 6
Solve and check.
a. 4x - 8 = 6x
b. 5(a + 2) - 3 = 22
Do Lesson 4.5 R. A. P. pages 117 & 118, 2-32 even.
Lesson 4.6 - ACTIVITY: Surface Area
Obj.: • draw a net for a solid figure. • recognize solid figures from their nets.
• find the surface area of a solid.
Vocabulary
• Net - A two-dimensional plane figure that can be cut and folded to make a model of
a solid shape.
• Surface area - The total area of all of the faces of a solid.
In this lesson, you will explore how to determine the amount of
material that is needed to make a package. Go to pages 119 & 120 of
the textbook.
Answer questions 1- 8 in the space below.
1. Cut out the net in Handout 4B.
2. Do. Find the area of each rectangle or
triangle and write it on your cut-out net.
8. a.____________________________
3. ______________________________
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4. Do.
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5. Do
b. ____________________________
c. ____________________________
6. ______________________________
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7. ______________________________
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**Practice for Lesson 4.6 pages 120 & 121, 1-11 all**
Lesson 4.7 - INVESTIGATION: Similar Figures—Perimeter,
Area, and Volume
Obj.: • determine the relationship that exists between the scale factor and
the ratio of the surface areas and volumes of two similar solids.
Vocabulary
• Similar solids - Solids that have the same shape. The ratios of their corresponding
linear measurements are equal.
• Lateral surface area - The surface area of the lateral faces of a solid that has one
or two bases.
In this lesson, you will examine two similar solids and explore the relationships
that exist between the scale factor and the ratios of the surface areas and the
volumes of the two similar solids. Go to pages 122 & 123 of the textbook.
Answer questions 1- 10 in the space below.
1. _____________________________
6. ______________________________
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2. _____________________________
7. ______________________________
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3. ______________________________
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10. a,_______ b.________ c. ________
EXAMPLE 1
Suppose the scale factor of two similar pyramids is 5 : 2. Find each of the following:
a. the ratio of the perimeters of the bases
b. the ratio of the areas of the bases
5:2
25 : 4
c. the ratio of the volumes of the pyramids
125 : 8
**Practice for Lesson 4.7 pages 124 & 125, 1-10 all**