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Geometry Review – Midterm Exam – Part 1 Name _____________________________ Vocabulary: Each vocabulary word will be described as a definition or a picture. You are responsible for all vocabulary words. Regular Polygon _________________________________________________________________________________________ Angle Bisector _________________________________________________________________________________________ Midpoint Formula _________________________________________________________________________________________ Scalene Ray _________________________________________________________________________________________ _________________________________________________________________________________________ Vertical Angles _________________________________________________________________________________________ Complementary Angles ___________________________________________________________________________________ Perpendicular Bisector _____________________________________________________________________________________ Supplementary Angles ______________________________________________________________________________________ Distance Formula _________________________________________________________________________________________ Chapter 1: 1) Use the diagram at the right to find the following. a) Three collinear points: ____, _____, ____. d) Intersection of AC and plane Q: _________. b) Four noncoplanar points ____, ____, ____, ____. e) Intersection of FB and plane Q: __________. c) Another name for plane Q: _____________. f) Intersection of AC and ED: ___________. 2) What is the intersection of plane AEFD and plane DCHF? 3) Name the angle in four different ways. 4) Solve for x if m < RQS = 6x + 20 and m < TQS = 2x + 4. Then find m < RQS and m < TQS. m < RQS = ________ x = _____________ m < TQS = ____________ 5) Ray GH bisects m < FGI. If m < FGH = (3x – 3)o and m < HGI = (4x – 14)o, solve for x and find m < FGH, m < HGI, and m < FGI. x = ________ m < FGH, = ________ m < HGI = __________ m < FGI = ___________ 6) Given the points P(-3, -3) and Q(5, -7): a) Find distance PQ to the nearest tenth. b) Find the midpoint of PQ. Chapter 2: 7) Identify the hypothesis and conclusion of the following conditional statement. If a student goes to CSU, then they go to school in Fort Collins. 8) Write the (a) converse, and (b) decide whether the converse is true or false. If two angles are vertical angles, then they are congruent. 9) What conclusion can you make from the two given statements? If three sides of one triangle are congruent to three sides of another, then the two triangles are congruent. If two triangles are congruent, then their corresponding parts are congruent. 10) Find the value of the variable. 11) Find the value of x. 12) Find the value of x and y. Geometry Review – Midterm Exam – Part 2 Name _____________________________ Vocabulary: Each vocabulary word will be described as a definition or a picture. You are responsible for all vocabulary words. Parallel Lines _________________________________________________________________________________________ Corresponding Angles _______________________________________________________________________________________ Hypotenuse _________________________________________________________________________________________ Same Side Interior Angles Alternate Interior Angles ________________________________________________________________________________ __________________________________________________________________________________ Scalene Triangle _________________________________________________________________________________________ Collinear ___________________________________________________________________________________ Isosceles Triangle _____________________________________________________________________________________ Transversal ______________________________________________________________________________________ Acute Triangle _________________________________________________________________________________________ Chapter 3: 1) Use the diagram at right to best describe each of the following pairs of angles. a) 13 and 16___________________ b) 2 and 14_____________________ c) 3 and 5_____________________ d) 8 and 14_____________________ e) 1 and 5____________________ f) 12 and 16 ____________________ 2) Find and then . Justify each answer. a) b) m <1= ______ by: ______________________________ m <1 = ______ by: ______________________________ m <2= ______ by: ______________________________ m <2 = ______ by: ______________________________ 3) Find the value of x in the following figures. A) B) C) 4) What is the measure of an interior angle of a regular 20-gon? 5) The exterior angle of a regular polygon is 20o. How many sides does the polygon have? 6) Find the value of the variable if a || b. Then find the values of the missing angles. x =______________ Top Angle = ___________ Bottom Angle = ____________ 7) Find the values of the missing variables. Chapter 4: 8) State the postulate or theorem you would use to prove each pair of triangles congruent. If the triangles cannot be proved congruent, write not possible. a) ___________________ b) _________________ c) __________________ d) __________________ e) _________________ 9) Find the missing angles in the figures below. m5 = ________ m1 = ________ m6 = ________ m2 = ________ m3 = ________ m4 = ________ m7 = ________ m8 = ________ 10) Find the values of x and y. 11) Given triangles XYZ ≅ EFG, EF = 3x + 7, XZ = 2x + 10 and XY = 6x – 11. 12) Find the value of x in the figure. Justify all steps. Statement Reason 1. KL = x+3, LM = 2x-1, KM = 5x-4 1. Given 2. KM = KL + LM 2. 3. 3. Substitution Property of Equality 4. 4. Combine Like Terms 5. 2x – 4 = 2 5. 6. 6. Addition Property of Equality 7. 7. Find XY. 13) Given: EG || DF , Prove: EG DF EDG FGD Statement Reason Chapter 8: 14) Solve for x. Round to the nearest tenth if necessary. a) b) 15) Use the rules for special right triangles to find missing variable. a) b) c) 16) Use trigonometry to solve for the missing variable. a) b) c) d) A 107-ft tall building casts a shadow of 90 ft. To the nearest whole degree, what is the angle of elevation to the sun?