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CHAPTER
8
Family Letter
Section B
What We Are Learning
Dear Family,
Closed Figures
In this section, your child will be learning about closed figures.
One special closed figure is a circle. A circle is defined as
being the set of points in a plane that are the same distance
from a given point called the center. A circle has a total
measure of 360° and is named by its center. Your child will
learn to identify the parts of a circle.
Vocabulary
These are the math words
we are learning:
acute triangle a triangle
with all angles less than
90°
Name all of the radii, diameters, and chords of circle S.
arc a part of a circle
named by its endpoints
Diameter:
, SB
, SC
, SD
SA
BD
Chords:
, DC
, AB
, BC
, BD
AD
center of the circle
the point inside a circle
that is the same distance
from all the points on the
circle
Radii:
D
S
A
central angle an angle
with its vertex at the
center of the circle
Polygons are another type of
common closed figures. A polygon is
C
B
a closed plane figure bounded by at
least three or more line segments.
The line segments are called sides, and the point at which the
line segments meet is called a vertex. Your child will learn to
identify polygons and justify why a figure is or is not a polygon.
chord a line segment
with endpoints on a circle
Determine whether each figure is a polygon. If it is
not, explain why not.
circle set of all points in a
plane that are the same
distance from a given
point
diameter a line segment
that passes through the
center of the circle with
endpoints on the circle
equilateral triangle
a triangle with three
congruent sides
isosceles triangle
a triangle where at least
two sides are congruent
obtuse triangle a triangle
where there is one obtuse
angle
parallelogram
a quadrilateral with two
pairs of parallel sides
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
A
B
C
D
A. This figure is a polygon.
B. This figure is not a polygon. The sides of a polygon must be
line segments.
C. The figure is not a polygon. The sides of a polygon cannot
intersect, except at the vertex.
D. This figure is not a polygon. A polygon must be a closed
figure.
Once a polygon is identified, your child will learn to categorize
it as either a regular or an irregular polygon. A regular
polygon is a polygon whose sides are congruent and whose
angles are congruent. A stop sign is an example of a regular
polygon.
65
Holt Mathematics
CHAPTER
8
Family Letter
Section B, continued
polygon a closed plane
figure formed by three or
more line segments
Triangles and quadrilaterals are two special groups of polygons
that your child will study in this section. Triangles can be
classified by their sides and by their angles.
radius a line segment
that connects a point on
the circle to the center of
the circle
Classify each triangle according to its sides and
angles.
rectangle a parallelogram
with four right angles
regular polygon
a polygon whose sides
and angles are all
congruent
rhombus a parallelogram
with four congruent sides
right triangle a triangle
with a right angle
right one right angle
scalene no congruent sides
This is a right scalene
triangle.
Quadrilaterals are polygons with four sides. Some
quadrilaterals may share properties, and therefore, may have
more than one name. Use the diagram below to help your child
recognize the unique properties of these special quadrilaterals.
QUADRILATERALS
A polygon with 4 sides and 4 angles
scalene triangle
a triangle with no
congruent sides
sector the part of a circle
that is enclosed by two
radii and the arc
connecting them
square a rectangle with
four congruent sides
trapezoid a quadrilateral
with exactly one pair of
parallel sides
acute all acute angles
isosceles 2 congruent sides
This is an acute
isosceles triangle.
PARALLELOGRAM
TRAPEZOID
KITE
A quadrilateral with
two pairs of parallel
sides.
Quadrilateral with
exactly one pair
of parallel sides.
Quadrilateral with
2 pairs of
adjacent
congruent sides.
RECTANGLE
RHOMBUS
A parallelogram
that has 4 right
angles.
A parallelogram that has 4
congruent sides.
SQUARE
A rectangle that has 4 congruent
sides or a rhombus with 4 right angles.
Have your child explain the differences and similarities between
the closed figures covered in this lesson.
Sincerely,
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
66
Holt Mathematics
Name
CHAPTER
8
Date
Class
Family Letter
Closed Figures
Name all of the radii, diameters, and chords of circle C.
Y
1. Radii
Z
2. Diameter
c
3. Chords
W
X
Determine whether each figure is a polygon. If it is not, explain
why not.
4.
5.
6.
8.
9.
Name each polygon.
7.
Classify each triangle according to its sides and angles.
10.
11.
12.
Give all of the names that apply to each quadrilateral.
13.
14.
15.
Find the measure of the unknown angle.
62°
25°
42°
x°
16.
17.
x°
; CX
; CZ
2. XZ
3. WX
; XZ
4. The figure is not a polygon. It is not bounded by line
Answers: 1. CY
segments. 5. The figure is a polygon. 6. The figure is not a polygon. A polygon must be a closed figure
7. pentagon 8. octagon 9. hexagon 10. acute equilateral 11. right scalene 12. obtuse isosceles
13. parallelogram; rectangle; rhombus; square. 14. parallelogram; rectangle 15. parallelogram; rhombus.
16. 76° 17. 65°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
67
Holt Mathematics
Name
CHAPTER
8
Date
Class
Family Fun
Creating the Universe
Materials
Number cube
Paper and pencil
Objectives
Be the first player to draw a complete universe. A complete universe
contains one of each item in the chart.
Directions
• Each player draws a large circle representing a universe.
• Take turns rolling the number cube. Use the chart to show what part of
the universe to draw. Be sure to label all points.
• You cannot draw a circle part unless the prerequisite is there. For
example, you may not draw a diameter or radius unless the center is
there, or a chord unless an arc or two points are there.
• Since the game continues until one player completes a universe, you
may have multiples of some circle parts, like diameters or points. Use a
strategy to decide where to place each circle part. Remember, the goal
is to be the first player to create an entire universe.
Number Rolled
Draw
1
Center
2
Diameter
3
Radius
4
Point
5
Arc (two points)
6
chord
Arc
Sector
Radius
Diameter
Points
Center
Chord
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
68
Holt Mathematics