Bellwork Solve for x Find three cities on this map that appear to be collinear.

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Presentation transcript:

Bellwork Solve for x Find three cities on this map that appear to be collinear

Bellwork Solution Solve for x

Bellwork Solution Find three cities on this map that appear to be collinear

Use Segments & Congruence Section 1.2

The Concept Today we’re going to discuss the concept of measurement of line segments We have to be aware that segments are the only line derivations that can be measured

Definitions Postulate Rule that is accepted without proof Can also be called an axiom Rule that is accepted without proof Postulate 1.2 Axis of symmetry Vertex

Ruler postulate This postulate explains that two points on a line can be explained as two coordinates The distance between the two coordinates correlates to the length of the segment A B x1 x2

Ruler Postulate uses One use is if we assign values to the coordinates B (2,0) x1 (12,0) x2 Or it can be used to allow the use of a ruler to find the length of a segment Seems nonsensical, but again is something that must be explained in order to base further exploration

Segment Addition Postulate This postulate explains that two connected segments created by a point between two others can be added together to get the full distance It can also be used to explain interior points If B is between A & C then AB+BC=AC If AB+BC=AC, then B is between A and C A B C

Segment Addition Postulate use Based on this postulate find the length of BC, if AC=32 A B C 13

Congruence Congruence The same measure as AB is congruent to CD Written as Important that congruence is used in lieu of equals

Nomenclature This denotes the segment AB At this point we should also discuss the two different nomenclatures you may see regarding segments This denotes the segment AB This denotes the length of segment AB

Use of Congruence Given the following points are XY and WZ congruent?

Homework 1.2 1, 2, 7-10, 12-20 even, 21-35, 37-45 odd

Example Point S is between R and T on RT. Find RS & ST RS=2x-8 ST=3x-10 RT=17

Most Important Points Definition of Postulate Ruler Postulate Segment Addition Postulate Definition of Congruence