AMSCO'S Geometry. New York - Rye High School

Review Exercises 1293-3 Proof • Deductive reasoning • Given • Prove • Two-column proof •Paragraph proof3-4 Direct proof • Indirect proof • Proof by contradiction3-5 Postulate • Axiom • Theorem • Reflexive property of equality •Symmetric property of equality • Transitive property of equality •Equivalence relation3-6 Substitution postulate3-7 Partition postulate • Addition postulate • Angle addition postulate •Subtraction postulate3-8 Multiplication postulate • Division postulate • Powers postulate • RootspostulateREVIEW EXERCISESIn 1–3, in each case: a. Write the given definition in a conditional form. b. Writethe converse of the statement given as an answer to part a. c. Write the biconditionalform of the definition.1. An obtuse triangle is a triangle that has one obtuse angle.2. Congruent angles are angles that have the same measure.3. Perpendicular lines are two lines that intersect to form right angles.4. Explain the difference between a postulate and a theorem.5. Name the property illustrated by the following statement:If AB CD, then CD AB.6. Is the relation “is greater than” an equivalence relation for the set of realnumbers? Explain your answer by demonstrating which (if any) of theproperties of an equivalence relation are true and which are false.In 7–12, in each case draw a figure that illustrates the given information andwrite a proof to show that the conclusion is valid.7. Given: AB g bisects CD at M.Prove: CM MD8. Given: RMST is a line segment, RM > MS, and MS > ST.Prove: RM > ST9. Given: ABCD is a line segment and AC > BD.Prove AB > CD10. Given: SQRP is a line segment and SQ RP.Prove: SR QP