1.3 Definitions and Postulates

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Presentation transcript:

1.3 Definitions and Postulates Honors Geometry

Lesson Focus We will see how numbers can be related to points on a line. This will show the ideas of distance, length , and congruence.

Definitions TERM DEFINITION GRAPHIC SYMBOL LINE SEGMENT Part of a line that is bounded by two distinct end points, and contains every point on the line between its end points 𝐴𝐵 LENGTH The distance between two endpoints of a line n/a The length of 𝐴𝐵 is denoted by AB RAY A line that extends infinitely from an endpoint OPPOSITE RAY Rays with the same endpoint that extend in opposite directions 𝑃𝑄 and 𝑃𝑅 are opposite rays

Guided Practice 1. Give 3 names for this line. _______________ 2. Name 2 line segments: _____________________ 3. Name 2 rays:_________________ 4. Name opposite rays: ______________

Definitions TERM DEFINTION GRAPHIC SYMBOL CONGRUENT SEGMENTS Two segments that have equal length MIDPOINT OF A SEGMENT A point that divides the segment into two congruent segments P is the midpoint of 𝐴𝐵 SEGMENT BISECTOR A line, segment, ray, or plane that intersects the segment at its midpoint Line l is the bisector of 𝐴𝐵 . 𝑃𝑄 and plane X also bisect 𝐴𝐵 .

Definitions Point P is between points A and B. This means P must like on 𝐴𝐵 . Postulates/Axioms are statements that are accepted without proof.

AB + BC = AC Postulate Postulate 2: Segment Addition Postulate If B is between A and C, then AB + BC = AC

Guided Practice B is between A and C with AB = x. BC = x + 6 and AC = 24. 1. Find the value of x. 2. Find BC.

Guided Practice T is the midpoint of 𝐿𝑀 . If LT = 4x +3 and MT= 2x + 9: 1. Evaluate for x. 2. Evaluate LT.

Guided Practice 3. Evaluate MT. 4. Evaluate LM.

NUMBER LINE On a number line, every point is paired with a number and every number is paired with a point.

RULER POSTULATE The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of the coordinates.

Finding the Length CG = 2. HK = The distance between two points can be found by subtracting the coordinates of its endpoints: CG = 2. HK =

Finding the Length

Guided Practice

Summary AB is a length. This is a number. AB = 4. 𝑅𝐺 is a ray where R is the endpoint. The arrowhead suggests that 𝑅𝐺 goes on past G. 𝑆𝑇 suggests that the line goes past S and T.