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Geometry Chapter 2 Test Review Name: _________________________ Date: _________________ Pd: _____ K 1. Given: m∠4 + m∠6 = 180o Prove: m∠5 = m∠6 4 5 6 J L Subtraction Property Statements Reasons Reflexive Property 1) m∠4 + m∠5 = 180o 1)_______________________ Substitution Property 2) m∠4 + m∠6 = 180o 2)________________________ Given 3) m∠4 + m∠5 = m∠4 + m∠6 3)________________________ Angle Addition Postulate 4) m∠4 = m∠4 4)________________________ Segment Addition Postulate 5) m∠5 = m∠6 5)_________________________ Definition of Complementary Angles Linear Pair Postulate 2. Create a symbolic representation for the given argument. Let p represent ∠A is 90° . Let q represent ∠B is 90° . is if and only if is or Therefore is is is . Answer Bank . and is . 3. Solve the equation. Justify each step. 4. Solve the equation. Justify each step. 5. Solve the equation for r. Justify each step. Solve for the variables. 6. 7. 20. Write the if-then form, the converse, the inverse and the contrapositive of the following statement. Then circle whether the statement is true or false. Vertical angles are congruent If-then: ___________________________________________________________________________________ ______________________________________________________________________________ True False Converse: ________________________________________________________________________________ ______________________________________________________________________________ True False Inverse___________________________________________________________________________________ ______________________________________________________________________________ True False Contrapositive_____________________________________________________________________________ ______________________________________________________________________________ True 21. If p represents “the sun is shining”, and q represents “people will dine outside”, write the following in words: a) : q → p _____________________________________________________________________ b) : p →: q _____________________________________________________________________ c) Write in symbolic notation: If people dine outside, then the sun is not shining. False 22. Write the converse of the following statement. If both statements are true, rewrite them as a bi-conditional statement. If a ray is a bisects an angle, then the ray cuts the angle into two congruent angles. Converse: ______________________________________________________________________True or False Biconditional:______________________________________________________________________________ Quadrilaterals Parallelograms Rectangles Squares Trapezoids Kites 23. Use the Venn Diagram above to help you determine whether the following statements are true or false. Provide a counterexample for questions you believe to be false. Explain those you claim to be true. a) If a quadrilateral is a rectangle, then it is a parallelogram. b) Some squares are rectangles. c) All trapezoids are parallelograms. 24. Use the law of syllogism to write a valid conclusion If you have a cell phone, then you text your friends. If you text your friends, then you will go to the party. Conclusion: _______________________________________________________________________________ 25. What can you conclude from the following two statements? If an angle measures less than 90o , then it is acute. m∠B = 63o Conclusion: _______________________________________________________________________________ 26. Use the following statement: If you are at the skate park, then you are a skateboarder. Label the Venn Diagram based on your conditional statement. Using the diagram, write one conclusion, if any, that can be drawn from the following statements: a) Bob is at the skate park.___________________________________________ b) Juanita is not a skateboarder._______________________________________ c) Sally is not at the skate park. _______________________________________ d) Billy is a skateboarder.____________________________________________ In the diagram, line QT is perpendicular to line RV, m<PWV = 70. Find the measures of the following: 27. Angle RWS __________ S R T 28. Angle SWT __________ U W 29. Angle QWV __________ 30. Angle RWP __________ Q P V Use the diagram to state the postulate that verifies the truth of the statement. Segment Addition Postulate A line contains at least two points. Angle Addition Postulate Two lines intersect at exactly one point. Through any two points there exists exactly one line A plane contains at least three noncollinear points. If two points lie in a plane, then the line containing them lies in the plane. The intersection of two planes is a line. Two lines are perpendicular if they form a right angle. 31. Line k and line l intersect at point B. 32. Points C, B, and D are on Plane M. 33. DE+EF=DF 34. Points C and F are on line p.