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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.

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

- 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.

1.2 All about Angles

- 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

- 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

- 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.

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