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Midterm Review 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 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 3) 4)Lines s, m and n are concurrent and lines s and m intersect line r at points X and Y. Find m Z. 5) State the degree(s) of rotational symmetry for a regular pentagon , 6) , , 7) The diagram at the right shows MOS with MOU . OE MS . If m SOE 58 and MOE SOE , find m M o 8) Which two points determine the perpendicular bisector of AB ? , Questions 9-11 refer to the diagram and two column proof below. Statements 1. K is the midpoint of Reasons HJ HK JK ( s. s.) 3. H J ( a. a.) 2. 4. HI 1. Given 2. 3. Given 4. JI IG 6. HI IF JI IG 5. IF 5. Given 6. or HF JG ( s. s.) 7. HFK JGK 8. FK GK 9) What reason best justifies statement (2) in the proof? 10) What reason best justifies statement (4) in the proof? 7. SAS Postulate (2,3,6) 8. Corresponding parts of congruent triangles are congruent. (7) 11) What reason best justifies statement (6) in the proof? 12) Given regular hexagon ABCDEF with center G, write a transformation that maps on to AGB . EGF 13) In the diagram at the right, which points which are coplanar. A) FDEAG B) CDAGH C) IHCDE D) CDF 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 ? 15)Find the degree measure of <REA in the figure at the right. (This question refers to acute REA outside pentagon GREAT) 16)Write sequence of rigid motions in function notation that maps ABC onto DEF . 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 18) For what values of x and y will MG and NJ be parallel? 19) 20)Write a transformation that maps quadrilateral AERO onto quadrilateral OBIC. 21)Given right TSE , GO 5x and GO 15x 12 . Find the length of GS . 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? 23) 24) 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 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? 26) The angle bisector of angle B goes through which point? 27)For what values of x and y will the lines L1 and L2 be perpendicular? Statements 1) 1 is supp. to 2 Reasons 1) 2) 3 1 2) 3) m 1 m 2 180 3) 4) m 3 m 1 4) 5) m 3 m 2 180 5) 6) 3 is supp. to 2 6) 28) and 29) Given: 7) AD || BC 7) 1 is supplementary to 2 3 1 Prove: 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 31) Given the figure at the right, find m FTO . 32) 33) . Find m z Answer Sheet No. 1 2 3 Answer 4 5 6 7 8 9 mZ 10 11 12 13 14 15 16 17 m UTY mM Name _____________________ Per_____________ No. 18 19 20 Answer X= 21 22 23 24 25 26 GS 27 28 29 m LMO m REA 30 31 32 33 y= *See Proof Statements 1-4 *See Statements 5-7 y= m FTO m z