Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x
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Transcript of Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x
Warm UpSolve.
1. x + 30 = 90
2. 103 + x = 180
3. 32 + x = 180
4. 90 = 61 + x
5. x + 20 = 90
Course 3
7-1 Points, Lines, Planes, and Angles
x = 60
x = 77
x = 148
x = 29
x = 70
Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza?
Course 3
7-1 Points, Lines, Planes, and Angles
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Learn to classify and name figures.
Course 3
7-1 Points, Lines, Planes, and Angles
TB P. 324-328
Vocabularypoint line plane
segment ray angle
right angle acute angle
obtuse angle complementary angles
supplementary angles
vertical angles
congruent
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Course 3
7-1 Points, Lines, Planes, and Angles
Course 3
7-1 Points, Lines, Planes, and Angles
Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.
Course 3
7-1 Points, Lines, Planes, and Angles
A point names a location.
• A Point A
Course 3
7-1 Points, Lines, Planes, and Angles
A line is perfectly straight and extends forever in both directions.
line l, or BCB
Cl
Course 3
7-1 Points, Lines, Planes, and Angles
A plane is a perfectly flat surface that extends forever in all directions.
plane P, or plane DEF
DE
F
PP
Course 3
7-1 Points, Lines, Planes, and Angles
G
HA segment, or line segment, is the part of a line between two points.
GH
Course 3
7-1 Points, Lines, Planes, and Angles
K
JA ray is a part of a line that starts at one point and extends forever in one direction.
KJ
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
A. Name 4 points in the figure.
B. Name a line in the figure.
Point J, point K, point L, and point M
Any 2 points on a line can be used.KL or JK
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
C. Name a plane in the figure.
Plane , plane JKL Any 3 points in the plane that form a triangle can be used.
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays
D. Name four segments in the figure.
E. Name four rays in the figure.KJ, KL, JK, LK
JK, KL, LM, JM
Course 3
7-1 Points, Lines, Planes, and Angles
An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees.
One degree, or 1°, is of a circle. m1
means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter.
1360
X
Y Z1 m1 = 50°
Course 3
7-1 Points, Lines, Planes, and Angles
The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.
F K J
G H
Course 3
7-1 Points, Lines, Planes, and Angles
The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°.
P
R QM
N
Course 3
7-1 Points, Lines, Planes, and Angles
A right angle measures 90°.
An acute angle measures less than 90°.
An obtuse angle measures greater than 90° and less than 180°.
Complementary angles have measures that add to 90°.
Supplementary angles have measures that add to 180°.
Course 3
7-1 Points, Lines, Planes, and Angles
A right angle can be labeled with a small box at the vertex.
Reading Math
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
A. Name a right angle in the figure.
B. Name two acute angles in the figure.
TQS
TQP, RQS
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
C. Name two obtuse angles in the figure.
SQP, RQT
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
D. Name a pair of complementary angles.
TQP, RQS mTQP + mRQS = 47° + 43° = 90°
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
E. Name two pairs of supplementary angles.
TQP, RQT
SQP, SQR
mTQP + mRQT = 47° + 133° = 180°
mSQP + mSQR = 137° + 43° = 180°
Course 3
7-1 Points, Lines, Planes, and Angles
Congruent figures have the same size and shape.
• Segments that have the same length are congruent.
• Angles that have the same measure are congruent.
• The symbol for congruence is , which is read “is congruent to.”
Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 3A: Finding the Measure of Vertical Angles
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
If m1 = 37°, find m3.
The measures of 1 and 2 are supplementary.
The measures of 2 and 3 are supplementary.
m2 = 180° – 37° = 143°
m3 = 180° – 143° = 37°
So m1 = m3 or m1 = m3. ~
Course 3
7-1 Points, Lines, Planes, and Angles
Additional Example 3B: Finding the Measure of Vertical Angles
In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
If m4 = y°, find m2.
m3 = 180° – y°
m2 = 180° – (180° – y°)
= 180° – 180° + y°
= y°
Distributive Property m2 = m4
So m4 = m2 or m4 m2.
Course 3
7-1 Points, Lines, Planes, and Angles
Lesson QuizIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
1. Name three points in the figure.
3. Name a right angle in the figure.
4. Name a pair of complementary angles.
5. If m1 = 47°, then find m3.
2. Name two lines in the figure.
Possible answer: A, B, and C
Possible answer: AGF
Possible answer: 1 and 2
47°
Possible answer: AD and BE