Introduction to Proof: Drawing Conclusions, part 2b

1. Introduction to Proof: Drawing Conclusions, part 2b Objectives: To draw conclusions about angles using given information To use the substitution and transitive properties GEOMETRY

2. Before we start, recall: GEOMETRY

3. If we know certain things about angles, we can discover other things about them. 105 105 A B If m  A = 105 and m B = 105, then __________________________________. If m A = m  B, then ____________. m  A = m  B  A   B GEOMETRY

4. Example 1 If HJ bisects GHI, then ______________. If  GHI   IHJ, then ________________. J I G H GEOMETRY

5. Drawing Conclusions If X Y and  YZ, then _______________________________. If  X Z, then __________________________________. GEOMETRY

6. Transitive Property of Congruence If XYand  Y Z, then _____. If ABCD and CD EF,___________. Example 2 If  AOBBOC and BOC COD, which other angles are congruent? GEOMETRY

7. Substitution Property of Equality If m A = m  B, then A can be substituted for B in any equation.. If AB = CD, then AB can be substituted for CD in any equation. GEOMETRY

8. Example 3 Given m  T = 53 and m  V = 53, by the substitution property, we can conclude ________________________________. Therefore, ________________________________. 53 53 V T GEOMETRY

9. Example 4 If GH = KL and KL = RT, then __________________________. You will use the transitive property and substitution property in showing relationships between angles or segments. GEOMETRY

10. Reading inGeometry Completion. You may need to draw and label diagrams to complete the statements which follow. If necessary, use the word bank below: GEOMETRY

11. Geometry often involves using information that is known to discover other _______________. This is called drawing __________. For example, if you know that AB _____  CAD, then you know that  CAB   BAD. Similarly, if P is the _________ of AB, then you know that AP  PB. GEOMETRY

12. Homework Assignment Drawing Conclusions WS GEOMETRY