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Carnegie 1.1. Point, Line, Plane. Three Undefined Terms. Point Line Plane These three terms are called undefined terms; we can only describe and create mathematical models to represent them. Point.

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Carnegie 1.1

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Carnegie 1 1

Carnegie 1.1

Point, Line, Plane


Three undefined terms

Three Undefined Terms

  • Point

  • Line

  • Plane

    These three terms are called undefined terms; we can only describe and create

    mathematical models to represent them.


Point

Point

  • A point is described as a location in space. A point has no size or shape but is often represented using a dot.


Carnegie 1 1

Line

  • A line is described as a straight continuous arrangement of an infinite number of

    points. A line has an infinite length, but no width. Arrowheads are used to indicate

    that a line extends infinitely in opposite directions.


More about lines

More about Lines

  • Line AB can be written using symbols as

    AB and is read as “line AB.”

    Collinear points are points that are located on the same line.


Plane

Plane

  • A plane is described as a flat surface. A plane has an infinite length and width but no depth. A plane extends infinitely in all directions. One model of a plane is the surface of a still body of water. Planes are determined by three points, but are usually named using one italic letter located near a corner of the plane as drawn.


Class work

Class Work

  • Complete Problems 1.1 and 1.3 before tomorrow.


Exit ticket

Exit Ticket

  • Summarize what Point, Line, Plane are.

  • Draw an example of a point, line, and plane be sure to name them properly.


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Ray

  • A ray is a portion of a line that begins with a single point and extends infinitely in one

  • direction. The endpoint of a ray is the single point where the ray begins.

  • A ray is named using two capital letters, the first representing the endpoint and

  • the second representing any other point on the ray. Ray AB can be written using

  • symbols as

    AB and is read as “ray AB.”


Line segment

Line Segment

  • A line segment is a portion of a line that includes two points and all of the collinear

  • points between the two points. The endpoints of a line segment are the points where the line segment begins and ends.

  • A line segment is named using two capital letters representing the two endpoints of the line segment. Line segment AB can be written using symbols as

  • ___

  • AB and is read as “line segment AB.”


Congruent line segments

Congruent Line Segments

  • If two line segments have equal measure, then the line segments have the same

    length. Congruent line segments are two or more line segments of equal measure.


1 2 all about angles

1.2 All about Angles

  • Naming Angles

  • Classifying Angles

  • Duplicating Angles

  • Bisecting Angles


Naming angles

Naming Angles

  • An angle is formed by two rays that share a common endpoint. The angle symbol is . The sides of an angle are the two rays. The vertex of an angle is the common endpoint of the two rays.


Classifying angles

Classifying Angles

  • An acute angle is an angle whose measure is greater than 0º, but less than 90º.


Right angles

Right Angles

  • A right angle is an angle whose measure is equal to 90º. A square drawn at the vertex is used to indicate a right angle in geometric figures.


Obtuse angles

Obtuse Angles

  • An obtuse angle is an angle whose measure is greater than 90º, but less than 180º.


Straight angle linear angle

Straight Angle/Linear Angle

  • A straight angle is an angle whose measure is equal to 180º. The sides of a straight angle form a line.


Congruent

Congruent

  • As with segments, use the congruent symbol, , between the geometric figure

  • angles, and the equal symbol, , between references to measures of angles.


Supplements and complements

Supplements and Complements

  • Two angles are supplementary angles if the sum of their angle measures is equal

    to 180º.


C omplementary a ngles

Complementary Angles

  • Two angles are Complementary angles if the sum of their angle measures is equal to 90º.


Perpendicular relationships

Perpendicular Relationships

  • Two lines, line segments, or rays are perpendicular if they intersect to form 90º angles. The perpendicular symbol is .


Adjacent angles

Adjacent Angles

  • Adjacent angles are two angles that share a common vertex and share a common side.


Linear pairs

Linear Pairs

  • A linear pair of angles are two adjacent angles that have noncommon sides that form a line.


Vertical angles

Vertical Angles

  • Vertical angles are two nonadjacent angles that are formed by two intersecting lines.


Class work1

Class Work

  • Students will complete problems 1.1, and 1.2 before class tomorrow.


1 3 special angles

1.3 Special Angles

  • Complements

  • Supplements

  • Midpoints

  • Perpendiculars

  • Perpendicular Bisectors


Supplements and complements1

Supplements and Complements

  • Two angles are supplementary angles if the sum of their angle measures is equal to 180º.


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  • Two angles are complementary angles if the sum of their angle measures is equal

  • to 90º.


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  • Two lines, line segments, or rays are perpendicular if they intersect to

  • form 90º angles. The perpendicular symbol is .


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  • The midpoint of a segment is a point that divides the segment into two congruent

  • segments, or two segments of equal measure.

  • P M Q

  • ___

  • PQ has midpoint M.

  • A segment bisector is a line, line segment, or ray that divides the line segment into

  • two line segments of equal measure, or two congruent line segments.

  • A perpendicular bisector is a line, line segment, or ray that intersects the midpoint

  • of a line segment at a 90 degree angle.


Adjacent angles1

Adjacent Angles

  • Adjacent angles are two angles that share a common vertex and share a

  • common side.


Linear pairs1

Linear Pairs

  • A linear pair of angles are two adjacent angles that have noncommon sides that

  • form a line.


Vertical angles1

Vertical Angles

  • Vertical angles are two nonadjacent angles that are formed by two

  • intersecting lines.


Your assignment for the day

Your Assignment for the day.

  • Students will complete problems 1,5,6,7 from section 3, students will be prepared to share their answers with the class when we meet next.


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