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Introduction to Proof: Drawing Conclusions, part 2b Objectives: To draw conclusions about angles using given information To use the substitution and transitive properties Mrs. McConaughy GEOMETRY 1 Before we start, recall: Measures are equal Parts are congruent m BAC = m DEF BAC DEF m AB = m CD AB CD AB = CD Mrs. McConaughy GEOMETRY 2 If we know certain things about angles, we can discover other things about them. 105 B A 105 If m A = 105 and m B = 105, m A = m B then __________________________________. If m A = m Mrs. McConaughy A B B, then ____________. GEOMETRY 3 Example 1 If HJ bisects GHI, then ______________. If GHI IHJ, then ________________. J I G Mrs. McConaughy GEOMETRY H 4 Drawing Conclusions If X Y and Y Z, then _______________________________. If X Z, then __________________________________. Mrs. McConaughy GEOMETRY 5 Transitive Property of Congruence If X Y and Y Z, then _____. If AB CD and CD EF,___________. Example 2 If AOB BOC and BOC COD, which other angles are congruent? Mrs. McConaughy GEOMETRY 6 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. Mrs. McConaughy GEOMETRY 7 Example 3 Given m T = 53 and m V = 53, by the substitution property, we can conclude ________________________________. Therefore, ________________________________. 53 53 Mrs. McConaughy T GEOMETRY V 8 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. Mrs. McConaughy GEOMETRY 9 Reading in Geometry Completion. You may need to draw and label diagrams to complete the statements which follow. If necessary, use the word bank below: midpoint conclusions midpoint Mrs. McConaughy bisects information pictures GEOMETRY 10 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. Mrs. McConaughy GEOMETRY 11 Homework Assignment Drawing Conclusions WS Mrs. McConaughy GEOMETRY 12