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Transcript
```7-1 Points, Lines, and Planes
Learn to describe figures by using the
terms of geometry.
Course 1
7-1 Points,
Insert Lesson
TitlePlanes
Here
Lines, and
Vocabulary
point
line
plane
line segment
ray
Course 1
7-1 Points, Lines, and Planes
The building blocks of geometry are points, lines, and planes.
A point is an exact location.
P
point P,
A point is named by a capital letter.
A line is a straight path that
extends without end in
opposite directions.
AB
A
B
BA
A line is named by two points on the line.
A plane is a flat surface that
extends without end in all
directions.
L
M
N
plane LMN,
plane MLN,
plane NLM
A plane is named by three points on
the plane that are not on the same line.
Course 1
7-1 Points, Lines, and Planes
A line segment is a line
and all the points between
the endpoints.
X
XY
YX
Y
A line segment is named by its endpoints.
A ray has one endpoint.
From the endpoint, the ray
extends without end in one
direction only.
J
K
ray JK, JK
A ray is named by its endpoint first
followed by another point on the ray.
Course 1
7-5 Triangles
Learn to classify triangles and solve
problems involving angle and side
measures of triangles.
Course 1
7-5 Triangles
Insert Lesson Title Here
Vocabulary
acute triangle
obtuse triangle
right triangle
scalene triangle
isosceles triangle
equilateral triangle
Course 1
7-5 Triangles
A triangle is a closed figure with three line
segments and three angles. Triangles can be
classified by the measures of their angles. An
acute triangle has only acute angles. An
obtuse triangle has one obtuse angle. A
right triangle has one right angle.
Acute triangle
Course 1
Obtuse triangle
Right triangle
7-5 Triangles
To decide whether a triangle is acute, obtuse,
or right, you need to know the measures of
its angles.
The sum of the measures of the
angles in any triangle is 180°.
You can see this if you tear the
corners from a triangle and
arrange them around a point on a
line.
By knowing the sum of the measures of
the angles in a triangle, you can find
unknown angle measures.
Course 1
7-5 Triangles
Sara designed this triangular trophy. The
measure of E is 38°, and the measure
of F is 52°. Classify the triangle.
To classify the triangle, find the
measure of D on the trophy.
E
D
F
m D = 180° – (38° +
52°)
m D = 180° – 90°Subtract the sum of the
known angle measures
m D = 90°
from 180°
So the measure of D is 90°. Because DEF has
one right angle, the trophy is a right triangle.
Course 1
7-5 Triangles
Triangles can be classified by the lengths
of their sides. A scalene triangle has no
congruent sides. An isosceles triangle
has at least two congruent sides. An
equilateral triangle has three congruent
sides.
Course 1
7-5 Triangles
Try This: Example 3
Classify the triangle. The sum of the lengths
of the sides is 21.6 in.
B
d + (7.2 + 7.2) = 21.6
d + 14.4 = 21.6
7.2 in.
7.2 in.
d + 14.4 – 14.4 = 21.6 – 14.4
d = 7.2
A
d
Side d is 7.2 inches long. Because ABC has
three congruent sides, it is equilateral.
Course 1
C
7-5 Triangles
Insert Lesson Title Here
Lesson Quiz
If the angles can form a triangle, classify the
triangle as acute, obtuse, or right.
1. 37°, 53°, 90°
right
acute
3. 61°, 78°, 41°
2. 65°, 110°,
not25°
a
triangle
obtuse
4. 115°, 25°, 40°
The lengths of three sides of a triangle are
given. Classify the triangle.
scalene
5. 12, 16, 25
6. 10, 10, 15
Course 1
isosceles
Learn to identify, classify, and compare
Course 1
Insert Lesson Title Here
Vocabulary
parallelogram
rectangle
rhombus
square
trapezoid
Course 1
figure with four sides and
four angles.
Five special types of
properties will be shown in
this lesson. The same mark
on two or more sides of a
figure indicates that the
sides are congruent.
Course 1
Parallelogram
Rectangle
Course 1
Opposite sides
are parallel and
congruent.
Opposite angles
are congruent.
Parallelogram
with four right
angles.
Rhombus
Square
Course 1
Parallelogram with
four congruent
sides.
Rectangle with
four congruent
sides.
Trapezoid
Course 1
exactly two parallel
sides. May have
two right angles.
Insert Lesson Title Here
Lesson Quiz
Complete each statement.
1. A quadrilateral with four right angles is a
_________.
square or rectangle
?
2. A parallelogram with four right angles and four
congruent sides is a _______.
?
square
3. A figure with 4 sides and 4 angles is a ______.
?
4. Give the most descriptive name for this
Course 1
7-7 Polygons
Learn to identify regular and not regular
polygons and to find the angle measures
of regular polygons.
Course 1
7-7 Polygons
Insert Lesson Title Here
Vocabulary
polygon
regular polygon
Course 1
7-7 Polygons
are examples of polygons.
A polygon is a closed
plane figure formed by
three or more line
segments. A regular
polygon is a polygon in
which all sides are
congruent and all angles
are congruent.
Polygons are named by the number of their
sides and angles.
Course 1
7-7 Polygons
Course 1
7-7 Polygons
Tell whether each shape is a polygon. If so,
give its name and tell whether it appears to
be regular or not regular.
A.
The shape is a closed plane figure formed
by 3 or more line segments.
polygon
There are 5 sides and 5 angles.
pentagon
All 5 sides do not appear to be congruent.
Not regular
Course 1
7-7 Polygons
Tell whether each shape is a polygon. If so,
give its name and tell whether it appears to
be regular or not regular.
B.
The shape is a closed plane figure
formed by 3 or more line segments.
polygon
There are 8 sides and 8 angles.
octagon
The sides and angles appear to be
congruent.
regular
Course 1
7-11 Symmetry
Learn to identify line symmetry.
Course 1
7-11 Symmetry
Insert Lesson Title Here
Vocabulary
line symmetry
line of symmetry
Course 1
7-11 Symmetry
A figure has line symmetry if it
can be folded or reflected so that
the two parts of the figure match,
or are congruent. The line of
reflection is called the line of
symmetry.
Course 1
7-11 Symmetry
Additional Example 1A: Identifying Lines of
Symmetry
Determine whether each dashed line appears
to be a line of symmetry.
A.
The two parts of the figure
appear to match exactly
when folded or reflected
across the line.
The line appears to be a line of symmetry.
Course 1
7-11 Symmetry
Additional Example 1B: Identifying Lines of
Symmetry
Determine whether each dashed line appears
to be a line of symmetry.
B.
The two parts of the figure
do not appear congruent.
The line does not appear to be a
line of symmetry.
Course 1
7-11 Symmetry
Try This: Example 1B
Determine whether each dashed line appears
to be a line of symmetry.
B.
The two parts of the figure
appear to match exactly
when folded or reflected
across the line.
The line appears to be a line of symmetry.
Course 1
7-11 Symmetry
Some figures have more than
one line of symmetry.
Course 1
7-11 Symmetry
Additional Example 2A: Finding Multiple Lines
of Symmetry
Find all of the lines of symmetry in the
regular polygon.
A.
Trace the figure and cut it out.
Fold the figure in half in
different ways.
Count the lines of symmetry.
5 lines of symmetry
Course 1
7-11 Symmetry
Additional Example 3A: Social Studies Application
Find all of the lines of symmetry in the flag.
There are no lines of symmetry.
Course 1
7-11 Symmetry
Additional Example 3B: Social Studies Application
Find all of the lines of symmetry in the flag.
B. Arizona
1 line of symmetry
Course 1
7-11 Symmetry
Additional Example 3C: Social Studies Application
Find all of the lines of symmetry in the flag.
1 line of symmetry
Course 1
7-11 Symmetry
Additional Example 3D: Social Studies Application
Find all of the lines of symmetry in the flag.
D. New Mexico
2 lines of symmetry
Course 1
7-11 Symmetry
Try This: Example 3A
Find all of the lines of symmetry in each design.
2 lines of symmetry
Course 1
7-11 Symmetry
Try This: Example 3B
Find all of the lines of symmetry in each design.
There are no lines of symmetry.
Course 1
7-11 Symmetry
Try This: Example 3C
Find all of the lines of symmetry in each design.
1 line of symmetry
Course 1
7-11 Symmetry
Insert Lesson Title Here
Lesson Quiz
Does the described figure have line symmetry?
1. right isosceles triangle
yes
2. rectangle
yes
Do the following capital letters of the alphabet
have symmetry? If so, is the line of symmetry
horizontal or vertical?
3. H yes, vertical and horizontal
Course 1
4. R no
```
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