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1 Name: Date: Geometry Midterm Review (C-Level) You must show all work to receiver full credit Chapter 1: Foundations of Geometry 1) Name the Plane: R 2) Name 3 collinear points: I A 3) Name 3 non-collinear points: F 4) Name all the rays in the plane: 5) If E is the midpoint of DF , DE = 2x + 4 and EF = 3x – 1. Find DE, EF, and DF. DE =___________________ EF=____________________ DF=____________________ 6) Find the length of KL. M x L 2.5x K _____________5x – 3 _______________ KL=____________________ 2 7) T is in the interior of PQR. Find each of the following. (Hint: Draw a diagram) a. mPQT if m PQR= 35º and m RQT =10 º. ________________________ b. m PQR if m PQR= (2x + 35)º, m RQT = (x – 5 )º and m PQT = (6x +10)º ________________________ c. m PQR if QT bisects PQR, m RQT = (3x+8)º and mPQT = (9x – 4 )º ________________________ 8) DEF and FEG are complementary. m DEF = (5y + 1) º, and m FEG = (3y – 7 )º. Find the measure of both angles. m DEF=________________ m FEG=________________ 9) DEF and FEG are supplementary. m DEF = (3z+12) º and mFEG = (7z – 32 )º. Find the measures of both angles. m DEF=_______________ m FEG=________________ 10) Use your knowledge of vertical angles to solve for x. (2x + 5)° 1 2 (4x – 5)° 11) What is the angle measure of 1 & 2? 3 12) Find a counterexample to show the conjecture is false. “Any number divisible by two is also divisible by 4.” A) 8 B) 16 C) 18 D) 20 13) If two lines intersect, they intersect in exactly ____________________________. 14) If two planes intersect, they intersect in exactly ___________________________. 15) Find the circumference and area of the circle with radius of 25m. Use 3.14 for pi. Round to nearest hundredth if necessary. C = ______________ A = ______________ 16) Find the area of the polygon. 12 ft 5ft 9ft 15ft A = ______________ 17) If A and B are supplementary angles and m A = ½ m B, find m A and m B. m A = ___________ m B = ___________ 18) Bisect the ABC A B C 4 Chapter 2: Geometry Reasoning 19) Write the converse, inverse, and contra positive of the conditional statement “If Stephanie’s birthday is January 1st, then she was born on New Year’s Day.” Find the truth-value of each. 20) For the conditional “If an angle is straight, then its measure is 180 degrees,” write the converse and the bi-conditional. 21) Determine if the bi-conditional “x2 = 100 if and only if x = 10” is true. If false, give a counterexample. 22) Test the statement to see if it is reversible. If so, write as a true bi-conditional statement. If not, write not reversible. “If lines intersect they intersect in exactly one point” is true. If false, give a counterexample. 23) Write the conditional, converse, inverse and contra positive of the statement: All rectangles have four right angles. 5 24) Write the definition “A scalene triangle is a triangle with three different side lengths” as a bi-conditional. 25) Change the following statement to a conditional statement: All even numbers are divisible by 2. 26) Identify the hypothesis and conclusion of the conditional. If a triangle has one angle greater than 90 degrees then it is an obtuse triangle. 27) Write the converse of the statement: “If it is Memorial Day, I do not have to go to school.” 28) Are the following statements true or false? If false, provide a counterexample. a. If it is Monday, then I have to go to school. b. If you have two right angles, then the angles are congruent. c. If a number is divisible by 3, then it is also divisible by 9. d. If you eat a piece of fruit, then it must have seeds. Chapter 3: Parallel and Perpendicular lines 29) Name all the segments that are parallel to BC E F C D 30) Name all segments that are perpendicular to BC H 31) Name a pair of skew lines. A 32) Name a pair of parallel planes. G B 6 k 1 2 m 3 4 5 6 7 8 mn n Use the diagram above for questions # 33 - 44 33) Name all pairs of vertical angles. 34) Name all pairs of same side interior angles 35) Name all pairs of corresponding angles. 36) Name all pairs of alternate interior angles. 37) Name all pairs of alternate exterior angles. 38) Name all pairs of same side exterior angles. 39) Name all angles that are supplementary to 1. 40) Line k is a transversal line of m and n. Name a pair of angles whose equality would guarantee that line m is parallel to line n. Then find the angle measures. Use the diagram above. 41) m4 = (8x – 34 )°; m 5 = (5x + 2)° m 4 = ___________ m 5 = ___________ 42) m 1 = (23x + 11)°; m 7 = (14x + 21)° m 1 = ___________ m 7 = ___________ 7 43) m 2 = (7x – 14)°; m 6 = (4x + 19)° m 2 = ___________ m 6 = ___________ 44) m 1 = (6x + 24)°; m 4 = (17x – 9) ° m 1 = ___________ m 4 = __________ s r 7 1 8 6 4 5 2 3 Use the diagram above for the following questions. Use the theorems and given information to show that r s . 45) 1 5 Converse of __________________________ 46) m3 m4 180 Converse of __________________________ 47) 3 7 Converse of __________________________ 48) m4 (13x 4); m8 (9 x 16); x 5 m 4 = _________________ m 8 = _________________ Converse of _________________________ 8 49) m8 (17 x 37); m7 (9 x 13); x 6 m 8 = _________________ m 7 = _________________ Converse of _________________________ 50) m2 (25 x 7); m6 (24 x 12); x 5 m 2 = _________________ m 6 = _________________ Converse of _________________________ 51) Given: p q Prove: m1 m3 180 1 Statement 2 3 Reason 1 p q 2 m 2 + m 3 =180° 3 1 2 4 Def. of Congruent Angles 5 52) Given: l m, 1 3 1 Prove: r p l Statement 2 p 3 r m Reason 1 2 3 Corresponding Angle Postulate 4 Transitive Property of Congruence 5 Converse of 9 Chapter 4: Triangle Congruencies 53) Label each diagram appropriately and identify which triangle congruence theorem satisfies the diagram. Choose from SSS, SAS, ASA, AAS, HL or not possible. If it is not possible explain why. Show all work; put a box around your answer. Triangles are not drawn to scale. a. Prove ABD ACD A B C D b. Prove ADC ABC D C A B c. Prove ABC DEC A A D A B A DEC d. Prove ABC E A C A A B BC C E E A D 10 54) Given: AC bisects BD BD bisects AC Prove: ΔAEB ΔCED Statement Reason 1 Given 2 Given 3 DE BE 4 AE CE 5 AEB DEC 6 B 55) Given: AB BC BD AC A D Prove: ABD CBD Statement Reason 1 2 3 Definition of Perpendicular Lines 4 Right Angle Theorem 5 6 BD BD C 11 M 56) Given: MJ NJ MJK NJK Prove: JMK JNK K J N Statement Reason N 1 2 3 Reflexive Property of Congruence 4 57) Find the measure of each angle. (2x+19)º (x+5)° 3x° 58) Find the measure of x. (2x + 3)° (4x – 7 )° 12 Miscelleaneous 59) Find the measure of R and P. P (2x – 10 )º R (4x – 34 )º m R:_____________ Q m P:_____________ 60) Find the value of x. (x)º Decide which of the given side lengths will form a triangle when constructed. Support your answer using the Triangle Inequality Theorem. 61) 6 ft, 8 ft, 10 ft 62) 4 m, 5 m, 9 m 63) 11 cm, 14 cm, 17 cm 64) Solve for the missing side. Round to nearest tenth if necessary. 8 ft 3 ft 13 65) Solve for the missing side. Round to the nearest tenth when necessary. 20 ft 15 ft 66) Sir Shrek is off to rescue Princess Fiona in the highest tower of the castle. He shoots an arrow with a 75 foot rope attached to it, to the top of the tower. Shrek is stand 20 feet away from the tower when he shoots the arrow. How tall is the tower he has to climb in order to rescue Princess Fiona? Round to the nearest tenth. 67) Find the midpoint of the following ordered pairs. a) A(1,2) & B(6, 8) Midpoint Formula x1 x 2 y1 y 2 , 2 2 b) C(0,-6) & D(4, 0) c) E(-4,-12) & F(6, -8) 68) If ABC DEF , state all corresponding segments and angles that are congruent. 9 69) Solve for x. Round to the nearest tenth. 12 60° 60° x 70) Find the length of line segment CD , if AB = 26; AE = 10 and m<C = 45°. Round to the nearest tenth. B C A E F D