pre-algebra 5-1 points, lines, planes, and angles learn to classify and name figures
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Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Learn to classify and name figures.
Pre-Algebra
5-1 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.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
A point names a location.
• A Point A
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
A line is perfectly straight and extends forever in both directions.
line l, or BCB
Cl
Pre-Algebra
5-1 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
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
G
HA segment, or line segment, is the part of a line between two points.
GH
Pre-Algebra
5-1 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
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 1A & 1B: 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
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 1C: 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.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 1D & 1E: 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
Pre-Algebra
5-1 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.
m∠1 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 m∠1 = 50°
Pre-Algebra
5-1 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
Pre-Algebra
5-1 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
Pre-Algebra
5-1 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°.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
A right angle can be labeled with a small box at the vertex.
Reading Math
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 2A & 2B: Classifying Angles
A. Name a right angle in the figure.
B. Name two acute angles in the figure.
∠TQS
∠TQP, ∠RQS
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 2C: Classifying Angles
C. Name two obtuse angles in the figure.
∠SQP, ∠RQT
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 2D: Classifying Angles
D. Name a pair of complementary angles.
∠TQP, ∠RQS m∠TQP + m∠RQS = 47° + 43° = 90°
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 2E: Classifying Angles
E. Name two pairs of supplementary angles.
∠TQP, ∠RQT
∠SQP, ∠RQS
m∠TQP + m∠RQT = 47° + 133° = 180°
m∠SQP + m∠RQS = 137° + 43° = 180°
Pre-Algebra
5-1 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.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Example 3A: Finding the Measure of Vertical Angles
In the figure, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles.
A. If m∠1 = 37°, find m∠3.
The measures of ∠1 and ∠2 add to 180° because they are supplementary, so m∠2 = 180° – 37° = 143°.
The measures of ∠2 and ∠3 add to 180° because they are supplementary, so m∠3 = 180° – 143° = 37°.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
A point names a location.
• A Point A
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
A line is perfectly straight and extends forever in both directions.
line l, or BCB
Cl
Pre-Algebra
5-1 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
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
G
HA segment, or line segment, is the part of a line between two points.
GH
Pre-Algebra
5-1 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
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
Try This: Example 1A & 1B
A. Name 4 points in the figure.
B. Name a line in the figure.
Point A, point B, point C, and point D
A B
CD
DA or BC Any 2 points on a line can be used.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
C. Name a plane in the figure.
Plane , plane ABC, plane BCD, plane CDA, or plane DAB
Any 3 points in the plane that form a triangle can be used.
A B
CD
Try This: Example 1C
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
D. Name four segments in the figure
E. Name four rays in the figureDA, AD, BC, CB
AB, BC, CD, DA
A B
CD
Try This: Example 1D & 1E
Pre-Algebra
5-1 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.
m∠1 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 m∠1 = 50°
Pre-Algebra
5-1 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
Pre-Algebra
5-1 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
Pre-Algebra
5-1 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°.
Pre-Algebra
5-1 Points, Lines, Planes, and Angles
A right angle can be labeled with a small box at the vertex.
Reading Math
Pre-Algebra
5-1 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.