1. Chapter 1 Lesson 4 Objective: To find the length of segments and measures of angles.

2. Postulate 1-5 Ruler Postulate The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B. 0 XY Since x is at -2 and Y is at 4, we can say the distance from X to Y or Y to X is: -2 – 4 = 6 or 4 – (-2) = 6

3. EXAMPLE 1 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

4. Postulate 1-6 Segment Addition Postulate If Q is between P and R, then PQ + QR = PR. PQ + QR = PR. If PQ +QR = PR, then Q is between P and R. PQ R 2x 4x + 6 PQ = 2x QR = 4x + 6 PR = 60 Use the Segment Addition Postulate find the measure of PQ and QR.

5. EXAMPLE 2 Find a length Use the diagram to find GH. Use the Segment Addition Postulate to write an equation. Then solve the equation to find GH. SOLUTION Segment Addition Postulate. Substitute 36 for FH and 21 for FG. Subtract 21 from each side. 21 + GH = 36 FG + GH=FH = 15GH

6. Angles Formed by 2 rays with the same endpoint –Vertex of the Angle Symbol: [  ] Name it by: –Its Vertex  A –A number  1 –Or by 3 Points  BAC – Vertex has to be in the middle A 1 B C

7. Ex.3: How many  s can you find? Name them. 3  s –  ADB or  BDA –  BDC or  CDB –  ADC or  CDA Notice D (the vertex) is always in the middle. Can’t use  D But  1 or  2 could be added. A B C D 1 2

8. Classifying Angles by their Measures Acute  Right  Obtuse  x°x° x < 90° x°x° x = 90° x°x° x > 90° Straight  x°x° x = 180°

9. Protractor Postulate P (1 – 7) Let OA & OB be opposite rays in a plane, & all the rays with endpoint O that can be drawn on one side of AB can be paired with the real number from 0 to 180. ABO D C

10. Angle Addition Postulate If point B is in the interior of  MAD, then m  MAB + m  BAD = m  MAD M B D A

11. If  MAD is a straight , then m  MAB + m  BAD = m  MAD = 180° m  MAB + m  BAD = m  MAD = 180° M B D A

12. Ex.4: Finding  measures Find m  TSW if – m  RSW = 130° –m  RST = 100° R S T W m  RST + m  TSW = m  RSW 100 + m  TSW = 130 m  TSW = 30°

13. Ex. 5  Addition Find x. m  XYZ = 150  1 = 3x - 15  2 = 2x - 10 x Y Z m  1 + m  2 = m  XYZ (3x - 15) + (2x – 10) = 150 5x – 25 = 150 5x = 175 x = 35

14. Assignment Page 29-30 #1-28 #42-64 Even