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Midterm Review (Answer Key) Per _____Name ___________________ o 1) In the diagram of SDU , m SDU 90 and m SUD 62 o . TY is drawn connecting points T and o Y on the triangle, such that m SYT 53 . Find m UTY m<UTY = 81o 2) Point P divides any triangle ABC into 6 triangles of equal area. To locate point P, what should one construct? A) Perpendicular bisectors B) Centroid C) Altitudes D) Incenter E) Parallel Lines B) Centroid *3) Write a conditional statement that is logically equivalent to “If the negotiations fail, the baseball strike will not end.” If the baseball strike ends, then the negotiations will not fail. 4)Lines s, m and n are concurrent and lines s and m intersect line r at points X and Y. Find m Z. m<Z = 74o 5) State the degree(s) of rotational symmetry for a regular pentagon 72o , 144o , 216o , 288o *6) Write a conditional statement, that is based on a theorem or definition, using the numbered angles below that would prove lines j and k parallel. Possible Answer: If 2 lines, such as j and k, are cut by a transversal forming congruent alternate interior angles, such as 2 and 7, then the lines are parallel. 7) The diagram at the right shows MOS with MOU . OE MS . If m SOE 58 and MOE SOE , find m M o m<M = 32o 8) Which two points determine the perpendicular bisector of 3 , AB ? 8 Questions 9-11 refer to the diagram and two column proof below. Statements Reasons 1. K is the midpoint of 1. Given HK JK 3. H J 2. 2. HJ ( s. s.) ( a. a.) 4. JI 5. IF IG 4. HI 6. 3. Given 5. Given HI IF JI IG 6. or HF JG ( s. s.) 7. HFK JGK 8. FK GK 7. SAS Postulate (2,3,6) 8. Corresponding parts of congruent triangles are congruent. (7) 9) What reason best justifies statement (2) in the proof? Definition of a midpoint – A midpoint divides a line segment into 2 congruent segments. 10) What reason best justifies statement (4) in the proof? Converse of the Isosceles Triangle Theorem – If two angles of a triangle are congruent, then the angles opposite those sides are congruent. 11) What reason best justifies statement (6) in the proof? Subtraction Postulate – If equal quantities are subtracted from equal quantities, the differences are equal. *12) Given regular hexagon ABCDEF with center G, write a transformation that maps triangle 4 onto triangle 6. TCG 4 6 or RG, 120o 4 6 are possible answers. *13) In the diagram at the right, list 3 points which are coplanar. Any 3 points, such as C, B, and D 14) In the diagram at the right, LMA is isosceles with LM AM , m L 37 o and m AMO 19o . What is m LMO ? m<LMO = 87o 15) Find the degree measure of <REA in the figure at the right. (This question refers to acute REA outside pentagon GREAT) m<REA = 70o 16) Write sequence of rigid motions in function notation that k.' o' p ' kop could potentially map sector onto sector r perp.bis.o 'k ' T kop ok ' PHI , m P x , m H 3x and m I 50 . Which statement is true? PHI is an equilateral triangle 17) In 2 (1) (2) PH < HI < PI (3) P H (4) PHI is an obtuse triangle (4) PHI is an obtuse triangle 18) For what values of x and y will MG and NJ be parallel? x 16 , y 20 19) (1) one *20) Write a transformation that maps quadrilateral AERO onto quadrilateral OBIC. TAO AERO OBIC 21) Given right TSE , GO 5x and GO 15x 12 . Find the length of GS GS = 18 22) Given the statement: “If the acute angles of a triangle are complementary, then the triangle is a right triangle.” What is the truth value about the statement and the truth value of its converse? True True 23) Given: GE AD FC Which is a valid conclusion? (1) GBC EBF (2) <ABF is complementary to <DBC (3) m<GBC +m<ABE =180o (4) m<FBE=m<GBA (1) GBC EBF 24) 2) Parallel 25) What is the difference between the sum of the measures of the interior angles of a regular octagon and the sum of the measures of the exterior angles of a regular octagaon? 720o 26) The angle bisector of angle B goes through which point? H 27) For what values of x and y will the lines L1 and L2 be perpendicular? x 10 , y 20 *28) and 29) Given: 1 is supplementary to 2 3 1 Prove: AD || BC Statements 1) Given 2) <3 <1 2) Given 3) m<1 + m<2 = 180 3) Definition of supplementary angles. (1) 4) m<3 = m<1 4) Definition of congruent angles. 5) m<3 + m<2 = 180 5) Substitution Postulate 6) <3 is supplementary to <2 6) Definition of supplementary angles. (5) 7) AD || BC 30) In the figure at the right, PA 3x 2 , PB 7 x 6 y and PC . Find the value of y. 2 y = 54 Reasons 1) <1 is supplementary <2 (2) (3, 4) 7) If two lines are cut by a transversal forming interior angles on the same side of the transversal that are supplementary then the lines are parallel. (6) 31) Given the figure at the right, find m FTO . m<FTO = 80o 32) . Find m z m<z = 131o 33) (2) Answer Sheet No. 1 Answer No. 18 Answer x = 16, y = 20 2 3 (B) Centroid 19 20 (1) One * T AERO OBIC 4 m Z 74 21 GS 18 5 6 72 , 144 , 216 , 288 * 7 m M 32o 22 23 24 True, True (1) <GBC <EBF (2) Parallel 8 9 10 11 12 3, 8 Definition of a midpoint 25 26 27 28 29 720o H x = 10, y = 20 *Proof *Proof 13 *Any 3 points such as CBD m LMO 87 m REA 70o 30 31 y = 54 14 32 m z 131o 33 (2) Rotation 15 16 17 m UTY 81o * If the baseball strike ends, then the negotiations will not fail. o o o o o Converse of the Isosceles Triangle Theorem Subtraction Postulate *T CG * r 4 6 perp.bis.o 'k ' o T kop ok ' (4) PHI is an obtuse triangle AO m FTO 80o