David Vundi Mathematics Teacher Use Segments and Congruence GEOMETRY

David Vundi Objective Use segment postulates and use the distance formula to measure distances

David Vundi Foundation of Geometry Postulate or axiom: a rule that is accepted without proof Theorem: a statement or rule which has been proven on the basis of previously established statements.

David Vundi Segment Addition A B C + = SEGMENT ADDITION POSTULATE. If B is between A and C then AB + BC = AC. If AB + BC = AC, then B is between A and C. AB BC AC

David Vundi Postulate 1 : Ruler Postulate This postulate allows for lengths to be measured The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB is the absolute value of the difference of the coordinates of A and B. AB = |a – b| or |b - a| A a B b

David Vundi Apply the Ruler Postulate Measure the length of ST to the nearest tenth of a centimeter. SOLUTION Align one mark of a metric ruler with S. Then estimate the coordinate of T. For example, if you align S with 2, T appears to align with 5.4. Use Ruler Postulate. ST = 5.4 – 2 = 3.4 The length of ST is about 3.4 centimeters. ANSWER

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

David Vundi Definitions to know Congruence vs. Equality Shapes vs. lengths Since lengths can be measured, lengths are equal – shapes are congruent.

David Vundi Using the Segment Addition Postulate M is between N and O. Find NO. 10 = 2x NM + MO = NO Seg. Add. Postulate 17 + (3x – 5) = 5x + 2 – 2 – 2 Substitute the given values Subtract 2 from both sides. Simplify. 3x + 12 = 5x + 2 3x + 10 = 5x –3x –3x 22 5 = x Simplify. Subtract 3x from both sides. Divide both sides by 2. EXAMPLE 3 NO = 5x + 2 Substitute 5 for x. Simplify. = 27 = 5(5) + 2

David Vundi M is between N and O. Find NO. NO = 5x + 2 Substitute 5 for x. Simplify. = 27 = 5(5) + 2 EXAMPLE 3 Continued

David Vundi Compare segments for congruence SOLUTION To find the length of a horizontal segment, find the absolute value of the difference of the x -coordinates of the endpoints. Use Ruler Postulate. JK = 2 – (– 3) = 5 Plot J(– 3, 4), K(2, 4), L(1, 3), and M(1, – 2) in a coordinate plane. Then determine whether JK and LM are congruent. LM = – 2 – 3 = 5 Use Ruler Postulate. JK and LM have the same length. So, JK LM. = ~ ANSWER

David Vundi A B C + = Find the length for AB and BC if AC = 60 and AB = 4x + 6 and BC= 6x (B is between A and C) + = AB BC AC AB BC AC 4x x + 14 = 60 4x + 6x = 60 10x + 20 = x = x = 4 Applying Segment Addition Postulate: Now finding AB and BC: AB = 4x + 6 BC = 6x + 14 = 4( ) + 6 = 6( ) = = 22 = = 38 Verifying the solution: = = 60 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

David Vundi E F G + = Find the length of EF and FG if EG = 80 and EF = 3x + 8 and FG= 7x (F is between E and G) + = EF FG EG EF FG EG 3x x + 12 = 80 3x + 7x = 80 10x + 20 = x = x = 6 Applying Segment Addition Postulate: Now finding EF and FG: EF = 3x + 8 FG = 7x + 12 = 3( ) + 8 = 7( ) = = 26 = = 54 Verifying the solution: = = 80 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

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