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B Geometry WS 2.2B Definitions and Biconditional Statements (p. 83; 25, 26, 32, 33, 59, 61) + Name: _______________________________ Date: __________________ Period: _______ Give a counterexample that demonstrates that the converse of the statement is false. 25) If two angles measure 42o and 48o, then they are complementary. Converse: ________________________________________________________________ Counterexample: ___________________________________________________________ 26) If Terry lives in Tampa, then she lives in Florida. Converse: ________________________________________________________________ Counterexample: ___________________________________________________________ Rewrite the true statement in if-then form and write the converse. If the converse is true, combine it with the if-then statement to form a true biconditional statement. If the converse is false, provide a counterexample. ex) If a polygon is a square it has four sides. Conditional:_If a polygon is a square, then it has four sides ______ T or F Converse: __If a polygon has four sides, then it is a square._____________ _____ T or F If TRUE: Biconditional statement: ____________________________________________________________________________________ If FALSE: Counterexample: _________If a polygon has four sides, then it is a rectangle.___________________________ 32) Adjacent angles share a common side. Conditional Statement: If _______________________, then _____________________________ T or F Converse: ________________________________, then ________________________________ T or F If TRUE: Biconditional statement: ______________________________________________________________________________________ If FALSE: Counterexample: ______________________________________________________________________________________ A) Two angles are congruent if they have the same measure. Conditional Statement: ______________________________________________________________ Converse: ____________________________________________________________________ T or F If TRUE: Biconditional statement: ____________________________________________________________________________________ If FALSE: Counterexample: _____________________________________________________________________________________ B) CA and CB are opposite rays if point C is between points A and B. Conditional Statement: _______________________________________________________________ Converse: ________________________________________________________________ T or F If TRUE: Biconditional statement: ____________________________________________________________________________________ If FALSE: Counterexample: _____________________________________________________________________________________ Find the measures of a complement and a supplement of the angle. 59. 87o complement = ________ supplement = ________ 61. 14o complement = ________ supplement = ________ Find the midpoint and the distance between points C( -3, 2) and D( 4, -6). Leave answer in exact form. (No decimals) Midpoint = _________________ Distance = _____________
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