1. http://mathematics-teacher.com David Vundi Mathematics Teacher http://mathematics-teacher.com Use Segments and Congruence GEOMETRY

2. http://mathematics-teacher.com David Vundi Objective Use segment postulates and use the distance formula to measure distances

3. http://mathematics-teacher.com 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.

4. http://mathematics-teacher.com 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

5. http://mathematics-teacher.com 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

6. http://mathematics-teacher.com 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

7. http://mathematics-teacher.com 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

8. http://mathematics-teacher.com David Vundi Definitions to know Congruence vs. Equality Shapes vs. lengths Since lengths can be measured, lengths are equal – shapes are congruent.

9. http://mathematics-teacher.com 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

10. http://mathematics-teacher.com 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

11. http://mathematics-teacher.com 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

12. http://mathematics-teacher.com David Vundi A B C + = Find the length for AB and BC if AC = 60 and AB = 4x + 6 and BC= 6x + 14. (B is between A and C) + = AB BC AC AB BC AC 4x +6 + 6x + 14 = 60 4x + 6x + 6 + 14 = 60 10x + 20 = 60 -20 10x = 40 10 x = 4 Applying Segment Addition Postulate: Now finding AB and BC: AB = 4x + 6 BC = 6x + 14 = 4( ) + 6 = 6( ) + 14 4 4 = 16 + 6 = 22 = 24 + 14 = 38 Verifying the solution: 22 + 38= 60 60 = 60 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

13. http://mathematics-teacher.com David Vundi E F G + = Find the length of EF and FG if EG = 80 and EF = 3x + 8 and FG= 7x + 12. (F is between E and G) + = EF FG EG EF FG EG 3x +8 + 7x + 12 = 80 3x + 7x + 8 + 12 = 80 10x + 20 = 80 -20 10x = 60 10 x = 6 Applying Segment Addition Postulate: Now finding EF and FG: EF = 3x + 8 FG = 7x + 12 = 3( ) + 8 = 7( ) + 12 6 6 = 18 + 8 = 26 = 42 + 12 = 54 Verifying the solution: 26 + 54= 80 80 = 80 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

14. http://mathematics-teacher.com David Vundi Enjoy your Life Everyday www.david-s.org