Vocabulary book review

Objectives Can you define and identify basic geometric terms?

Undefined Terms Undefined Terms: terms that do not have any actual size TermDefinitionNaming TermPicture Point A location in space, no actual shape or size By a capital letter Point A Line Made up of two points and has no thickness or width; 1 dimension By any two points on the line or small italic letter Line AB Line l Plane A flat surface made up of points that extends indefinitely in all directions; 2 dimensions By any three noncollinear points or large italic letter Plane DMP Plane L A

Vocabulary TermDefinitionPicture Collinear If points are on the same line, then they are collinear Coplanar If points are on the same plane, then they are coplanar IntersectionSet of points in common for two or more figures

Possibilities of Intersection of a Plane and a Line (add to facts of line or plane) Three possibilities: Line passes through the plane—intersection is a point Line lies on the plane—intersection is a line Line is parallel to the plane—no common points

Intersection of Two Planes or Two Lines (add to facts of lines and planes) Intersection of two lines is a point Intersection of two planes is a line

Examples Name a plane. Name a point. Name a line. Name three points that are collinear. What point do line j and line m intersect at? Two lines intersect in a ____________ Two planes intersect in a ______________ A line and a plane intersect in a _____________

Example How many planes are in the figure? Are points A,B,C coplanar? Are points A,B,C,F coplanar?

Example How many planes are labeled in the figure? Name the plane containing points E and C. Name the intersection of plane R and plane P. Name a point that is collinear to D and A. Name a point that is not coplanar to F, D, and G.

Example Draw two planes not intersecting. Draw a line on a plane. Draw a line intersecting a plane. Draw three lines that are not coplanar.

TermDefinitionNaming TermsPicture Line SegmentPart of a line that has two endpoints Segment AB AB Betweenness of Points If B is between points A and C (A-B-C), then A, B, and C are collinear and AB+BC=AC Relationship of points Midpoint of a Segment The point halfway between the endpoints of the segment If A-B-C and AB=BC then B is the midpoint of AC Congruent Segments If two segments are congruent then they have the same length Segment BisectorAny segment, line, or plane that intersects a segment at its midpoint Segment Vocabulary

Angle Vocabulary TermDefinitionNaming the Term/ Symbol Picture RayA part of a line that has one endpoint and extends in one direction AngleFormed by two noncollinear rays that have a common endpoint Sides of the angle are rays Vertex of the angle is the common endpoint Angles are measured in degrees Name this angle. Either use 3 or 1 letter or 1 number Order matters in naming an angle! Symbol for angle

Angle Terms and Types TermDefinitionPicture Right angle If an angle measures 90 degrees then it is a right angle Acute Angle If an angle measures less than 90 degrees then it is an acute angle Obtuse Angle If an angle measures more than 90 degrees then it is an obtuse angle Straight Angle If an angle measures 180 degrees then it is a straight angle Congruent Angles If two angles are congruent then they have the same measure Angle Bisector If a ray divides an angle into two congruent angles then it bisects the angle

1) Find the length of segment EG. ● ● ● 2) Find the length of segment AB. AC=15 ● ● ● 3) Find the midpoint of AB. 4) Find x, if B is between A and C. AB=2x, BC=3x, and AC=15. Examples EF G A B C

Measuring an Angle Use a protractor

Examples 1)Name all angles with vertex B. 2)Name the sides of angle 5. 3)Write another name for angle 6. 4)Name a point on the exterior of Angle GBA. 5) Are ray BD and ray BG the same ray? G E A 5 F 6 B D

Classwork Complete practice sheet 1.2 and 1.3

TermDefinitionPicture Adjacent AnglesIf two angles have a common vertex and a common side then they are adjacent Linear PairIf there is a pair of adjacent angles with noncommon sides that are opposite rays, then there is a linear pair formed Vertical AnglesIf there are two nonadjacent angles formed by two intersecting lines, then vertical angles are formed Vertical angles are congruent Special Angle Pairs

TermDefinition/Relationsh ip Picture Complementary Angles If two angles add up to 90 degrees, then they are complementary Supplementary Angles If two angles add up to 180 degrees then they are supplementary Linear pair angles are supplementary Angle Relationships

TermDefinitionSymbolPicture Perpendicular Lines Lines that intersect to form four right angles. All angles are congruent and adjacent. Right angle symbol indicates perpendicular. Parallel LinesCoplanar lines that do not intersect. Skew LinesLines that do not intersect and are not coplanar. Types of Lines

Match the following term with the appropriate picture Adjacent angles Linear Pair Vertical Angles Complementary Angles Supplementary Angles Perpendicular Lines Examples

Name two adjacent angles, two vertical angles, two supplementary angles, and a linear pair Find x. Examples

TermDefinitionPicture PolygonA closed figure formed by a finite number of coplanar segments called sides Convex A polygon (which is straight-sided) is convex if there are no "dents" or indentations in it (no internal angle is greater than 180°) Concave A polygon (which is straight-sided) is concave if there are "dents" or indentations in it (where the internal angle is greater than 180°) (Caves in) RegularAll sides are congruent and all angles are congruent TriangleA three sided polygon Angles add to 180 degrees Vocabulary

Types of Triangles By Angles Name by AnglesPicture Acute Triangle 3 Acute angles Equiangular Triangle 3 congruent angles Obtuse Triangle One obtuse angle Right Triangle One right angle

Types of Triangles By Sides Names by SidesPicture Equilateral Triangle 3 congruent sides Isosceles Triangle 2 congruent sides Scalene Triangle No congruent sides

Can be AssumedCannot be Assumed All points are coplanarPerpendicular lines: BX FX A, X, D are collinear BX, FX, DX, AX, GX, EX intersect at X X is between A and D E is in the interior of angle GXD Angle AXG and Angle GXE are adjacent Angle AXB and Angle BXD are supplementary Interpreting Diagrams