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# Carnegie 1.1 - PowerPoint PPT Presentation

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

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

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

### 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.

• 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

• 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

• Complete Problems 1.1 and 1.3 before tomorrow.

### Exit Ticket

• Summarize what Point, Line, Plane are.

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

### 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

• 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

• 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.

• Naming Angles

• Classifying Angles

• Duplicating Angles

• Bisecting 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

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

### 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

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

### 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

• 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

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

to 180º.

### Complementary Angles

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

### Perpendicular Relationships

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

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

### Linear Pairs

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

### Vertical Angles

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

### Class Work

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

### 1.3 Special Angles

• Complements

• Supplements

• Midpoints

• Perpendiculars

• Perpendicular Bisectors

### Supplements and Complements

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

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

• to 90º.

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

• form 90º angles. The perpendicular symbol is .

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

• common side.

### Linear Pairs

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

• form a line.

### Vertical Angles

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

• intersecting lines.

### 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.