Carnegie 1.1

Carnegie 1.1Point, Line, PlaneThree Undefined TermsPointLinePlane These three terms are called undefined terms; we can only describe and createmathematical models to represent them.PointA point is described as a location in space. A point has no size or shape but is often represented using a dot.LineA line is described as a straight continuous arrangement of an infinite number ofpoints. A line has an infinite length, but no width. Arrowheads are used to indicatethat a line extends infinitely in opposite directions.More about LinesLine 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.PlaneA 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 TicketSummarize what Point, Line, Plane are.Draw an example of a point, line, and plane be sure to name them properly.RayA ray is a portion of a line that begins with a single point and extends infinitely in onedirection. 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 andthe second representing any other point on the ray. Ray AB can be written usingsymbols as AB and is read as ray AB.Line SegmentA line segment is a portion of a line that includes two points and all of the collinearpoints 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 SegmentsIf two line segments have equal measure, then the line segments have the samelength. Congruent line segments are two or more line segments of equal measure.1.2 All about AnglesNaming AnglesClassifying AnglesDuplicating AnglesBisecting AnglesNaming AnglesAn 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 AnglesAn acute angle is an angle whose measure is greater than 0, but less than 90.

Right AnglesA right angle is an angle whose measure is equal to 90. A square drawn at the vertex is used to indicate a right angle in geometric figures.Obtuse AnglesAn obtuse angle is an angle whose measure is greater than 90, but less than 180.

Straight Angle/Linear AngleA straight angle is an angle whose measure is equal to 180. The sides of a straight angle form a line.

CongruentAs with segments, use the congruent symbol, , between the geometric figureangles, and the equal symbol, , between references to measures of angles.

Supplements and ComplementsTwo angles are supplementary angles if the sum of their angle measures is equalto 180.Complementary AnglesTwo angles are Complementary angles if the sum of their angle measures is equal to 90.Perpendicular RelationshipsTwo lines, line segments, or rays are perpendicular if they intersect to form 90 angles. The perpendicular symbol is .Adjacent AnglesAdjacent angles are two angles that share a common vertex and share a common side.Linear PairsA linear pair of angles are two adjacent angles that have noncommon sides that form a line.Vertical AnglesVertical angles are two nonadjacent angles that are formed by two intersecting lines.Class WorkStudents will complete problems 1.1, and 1.2 before class tomorrow.1.3 Special AnglesComplementsSupplementsMidpointsPerpendicularsPerpendicular BisectorsSupplements and ComplementsTwo angles are supplementary angles if the sum of their angle measures is equal to 180.Two angles are complementary angles if the sum of their angle measures is equalto 90.Two lines, line segments, or rays are perpendicular if they intersect toform 90 angles. The perpendicular symbol is .The midpoint of a segment is a point that divides the segment into two congruentsegments, 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 intotwo line segments of equal measure, or two congruent line segments.A perpendicular bisector is a line, line segment, or ray that intersects the midpointof a line segment at a 90 degree angle.Adjacent AnglesAdjacent angles are two angles that share a common vertex and share acommon side.Linear PairsA linear pair of angles are two adjacent angles that have noncommon sides thatform a line.Vertical AnglesVertical angles are two nonadjacent angles that are formed by twointersecting 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.