1. Do Now In the diagram of collinear points, DH = 35, GH = 20, DE = EF = FG. Find each length. (Picture not drawn to scale).   DE =   EF =   FG =   DF =   EG =   FH =   DG = D E F G H *Always go by information given, not the drawn figure.

2. Homework Worksheet Need extra help? Book: 2.2 & 2.6

3. Unit 1: Basics of Geometry Day 3: Measuring Segments & Angles

4. Objective To use measurement postulates to find measure of segments and angles

5. Segment Addition Postulate ABC AB + BC = AC The length of two smaller, adjacent, collinear segments add up to the larger segment. Segment Notations: AB AB Length of AB Used with measurements/lengths Refers to the figure/shape

6. Angle Addition Postulate A B C D m  ABC + m  CBD = m  ABD The degree measure of two smaller, adjacent, angles add up to the measure of the larger angle. Angle Notations: m  ABC Measure of  ABC Used with degrees  ABC Refers to the figure/shape

7. Angle Addition Postulate Point L is on the interior of  KJM. If m  KJM = 145 o, m  KJL = (6x) o, and m  LJM = (3x+10) o, find x. K J M L 145 o 6x o 3x+10 o m  KJL + m  LJM = m  KJM 6x+ 3x + 10 = 145 9x + 10 = 145 x = 15 *Always check your answer by plugging it into the expressions. *Note the marking for the entire angle.

8. Definitions Postulate: An undefined rule that is accepted as true without proof Theorem: A statement that must be proved to be true

9. Linear Pair Postulate If two angles form a linear pair, then they are supplementary. Vertical angles are congruent 1 2 m  1 + m  2 = 180 o Vertical Angles Theorem 1 2 3 4 m  1 = m  3 m  2 = m  4 *Congruent: same size & shape

10. Solve for all the variables. 3(6z + 7) o 5(2z + 9) o (4y-35) o 5(2z + 9) = 3(6z + 7) 10z + 45 = 18z + 21 24 = 8z 3 = z 75 o 105 o 4y – 35 = 105 4y = 140 y = 35

11. Find the measure of all angles.  A is supplementary to  B and complementary to  C. *check to make sure your answers make sense with the problem

12. Did you meet today’s objective? Describe the segment/angle addition postulate Define complementary Define supplementary How do you identify linear pairs? What is their special property? How do you identify vertical angles? What is their special property?