1.1:Identify Points, Lines, & Planes 1.2:Use Segments & Congruence Objectives: 1.To learn the terminology and notation of the basic building blocks of geometry. 2.To use the Ruler and Segment Addition Postulates

Vocabulary PointLine Segment LineRay Plane As a group, define each of these without your book. Draw a picture for each word and leave a bit of space for additions and revisions.

Undefined Terms? What the Ancient Greeks said: “A point is that which has no part. A line is breadthless length.” undefined terms In geometry, we always try to define things in simpler terms. Point, line, and plane are considered undefined terms, however, and cannot be made any simpler, so we just describe them.

Undefined Terms? undefined terms In geometry, we always try to define things in simpler terms. Point, line, and plane are considered undefined terms, however, and cannot be made any simpler, so we just describe them. What the Ancient Chinese said: “The line is divided into parts, and that part which has no remaining part is a point.”

Points Basic unit of geometry No size, only location Represented by a dot and named by a CAPITAL letter Mathematical model of a point

Points A star is a physical model of a point

Lines Straight arrangement of points No width, only length Extends forever in 2 directions Named by two points on the line: line AB or BA or or Mathematical model of a line

Lines Spaghetti is a physical model of a line

Lines How many lines can you draw through any two points? Mathematical model of a line

Collinear Points Collinear pointsCollinear points are points that --?--. –Points A, B, and C are collinear

Planes Flat surface that extends forever Length and width but no height Represented by a 4- sided figure and named by a capital script letter or 3 letters on the same plane. Mathematical model of a plane

Planes Flattened dough is a physical model of a plane

Planes How many points does it take to define a plane? Mathematical model of a plane

Coplanar Points Coplanar pointsCoplanar points are points that --?--. –Points A, B, and C are coplanar

Hierarchy of Building Blocks 0-D 1-D 2-D 3-D Space Space is the set of all points

Example 1 1.Give two other names for and plane R. 2.Name three points that are collinear. 3.Name four points that are coplanar.

Line Segment line segmentA line segment consists of two endpoints and all the collinear points between them. –Line segment AB or Endpoints

Congruent Segments Congruent segmentsCongruent segments are line segments that have the same length.

Ray rayA ray consists of an endpoint and all of the collinear points to one side of that endpoint. –Ray AB or A laser is a physical model of a ray

Example 2 Ray BA and ray BC are considered opposite rays. Use the picture to explain why. At what time would the hands of a clock form opposite rays?

Example 3 1.Give another name for. 2.Name all rays with endpoint J. Which of these rays are opposite rays?

Intersection intersect intersectionTwo or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common. The intersection of two lines is a point. The intersection of two planes is a line.

Example 4 What is the length of segment AB? A B

Example 4 You basically used the Ruler Postulate to find the length of the segment, where A corresponds to 0 and B corresponds to 6.5. So AB = |6.5 – 0| = 6.5 cm A B

Example 5 Now what is the length of ? A B

Ruler Postulate coordinate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is its coordinate. distance The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.

Example 6 When asked to measure the segment below, Kenny gave the answer 2.7 inches. Explain what is wrong with Kenny’s measurement.

Give Them an Inch… A Standard English ruler has 12 inches. Each inch is divided into parts. Cut an inch in half, and you’ve got 1/2 an inch. Cut that in half, and you’ve got 1/4 an inch. Cut that in half, and you’ve got 1/8 inch. Cut that in half, and you’ve got 1/16 inch. Click me!

Example 7 Use the diagram to find GH.

Example 7 Use the diagram to find GH. Could you as easily find GH if G was not collinear with F and H? Why or why not?

Segment Addition Postulate betweenIf B is between A and C, then AB + BC = AC. betweenIf AB + BC = AC, then B is between A and C.

Example 8 Point A is between S and M. Find x if SA = 2 x – 5, AM = 7 x + 3, and SM = 25.

Example 9 Point E is between J and R. Find JE given that JE = x 2, ER = 2 x, and JR = 8.

Example 10: SAT Points E, F, and G all lie on line m, with E to the left of F. EF = 10, FG = 8, and EG > FG. What is EG?

Example 11 Given that AB = CD, what other pair of segments must also have equal lengths?