Lesson 1-3 Segments, Rays, & Distance (page 11) Essential Question How are the relationships of geometric figures used in real life situations?

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Presentation transcript:

Lesson 1-3 Segments, Rays, & Distance (page 11) Essential Question How are the relationships of geometric figures used in real life situations?

Point B is _______________ A and C if it lies on line AC (________). ABC SEGMENT: consists of points A and C and all points that are __________ A & C. example:AC RAY: consists of and all other points P such that C is ___________ A & P. example:ACP between..... endpoint

OPPOSITE RAYS: 2 rays that have the same _______________ and form a line. example:XOY Geometry and Algebra are brought together with the ______________ line. A B C D E F G H I J | ||||||||| HIJKLMNO || | | | | | | PQRSTUVW || | | | | | | endpoint number...

A BCDEFGHIJ | | | | | | | | | | Every point is paired with a _______________. Every number is paired with a ___________. 1 - to - 1 Correspondence A corresponds to ______, B corresponds to ______, etc. A ⇔ ______ B ⇔ ______ LENGTH (of a segment): the __________________ between its endpoints. AB means the _____________ of or the ________________ between points A & B. AB = ∣ a - b ∣ = ∣ b - a ∣ number point distance length distance point coordinate

A BCDEFGHIJ | | | | | | | | | | AB = ∣ a - b ∣ = ∣ b - a ∣ examples: CH = ________ 5

A BCDEFGHIJ | | | | | | | | | | AB = ∣ a - b ∣ = ∣ b - a ∣ examples: AJ = ________ 9

A BCDEFGHIJ | | | | | | | | | | AB = ∣ a - b ∣ = ∣ b - a ∣ examples: BF = ________ 4

AB = ∣ a - b ∣ = ∣ b - a ∣ POSTULATE (axiom): statement accepted without ________. RULER POSTULATE (1)The points on a line can be paired with the real numbers in such a way that any two points can have coordinates _____ and _____. (coordinatized line) (2)Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their _______________. (distance) POSTULATE 1 proof 01 coordinates

SEGMENT ADDITION POSTULATE If B is between A and C, then: AB + BC = _________. ABC POSTULATE 2 example: Given the diagram with AC = 23, AB = 2x, and BC = x - 1, find x, AB, and BC. x = ______ AB = _____ BC = _____ AC AB + BC = AC 2x + x -1 = 23 3x = 24 x = 8 8 AB = 2x AB = 2*8 AB = BC = x - 1 BC = BC = = 23 ✔ WHY?

CONGRUENT: objects that have the same _________ and ___________. CONGRUENT SEGMENTS: segments that have equal ______________. example:A C AB CD B D _______ expresses a relationship between numbers. _______ expresses a relationship between geometric figures, NOT numbers. sizeshape length = = ≅

MIDPOINT of a SEGMENT: the point that divides the segment into ________ congruent segments. example:AMB AM ______ MB, then  M is the ________________ of BISECTOR of a SEGMENT: a_________, _______________, ________, or plane that intersects the segment at its midpoint. two = midpoint line segmentray...

Assignment Written Exercises on pages 15 & 16 RECOMMENDED: 1 to 25 odd numbers REQUIRED: 27 to 47 odd numbers & 46 How are the relationships of geometric figures used in real life situations?