Geometry Semester 1 Final Exam Review

Transcription

1 Name: ate: Per: Geometry Semester 1 Final Exam Review Chapter 1: Tools of Geometry 1) Find a pattern for the sequence. Use the pattern to show the next three terms. 15, 12, 9, 6, 2) If two lines intersect, then they intersect in a. 3) If two planes intersect, then they intersect in a. 4) Which of the following could not be the intersection of two planes? a. B b. B c. B d. BC e. point 5) B is the midpoint of C. If B 2x 1 and BC 3x 4, what is x? What is the measure of BC? What is the measure of C? 6) Find the midpoint and distance on a number line between 6 and ) S is between R and T. If RT 64, RS 3x 1 and ST 2x 2, find x. 8) raw an example of each of the following a. Complementary b. Supplementary c. Vertical angles d. djacent ngles angles angles 9) m RST 2x 8, m TSW 3x 14, m RSW 7x 2. Find m TSW.

2 10) Find m RQS. 2x 4 6x 20 T Q R 11) Find the value of x. 3x 31 2x 6 S 12) Find TO given TO 2x 12 OP x 5 TP 50 T O P 13) What is the measure of this angle? How would you classify the angle? 14) EM bisects GEO m GEM 3x 5 m MEO x 29 Find m GEO. 15) m GIT 2x 15 m FIT x m GIF 4x 5 Find m GIT. I G T F 16) Given the points 2, 4 and 5,1 : a. Find the distance between the points. b. Find the midpoint between the points.

3 17) Given the points 6, 5 and 3,2 : a. Find the distance between the points to the nearest tenth. b. Find the midpoint between the points. 18) O is the midpoint of G. Find the coordinate of G if O is 7 and is 3. 19) Which is the missing endpoint if the midpoint is 0, 6 and the other endpoint is 3,8? a. (1.5, 1) b. (1, 1.5) c. (-3, -20) d. (20,-3) 20) I. What is the circumference of a circle with: (Leave answers in form) a. Radius of 4 cm b. diameter of 32 cm II. What is the area of a circle with: (Leave answers in form) b. Radius of 4 cm b. diameter of 32 cm 21) The perimeter of a rectangle is 28 feet and the base is 8 feet. What is the height? 22) The area of a rectangle is 2 54 cm and the height is 9 cm. What is the base?

4 Chapter 2: Reasoning and Proof 23) Given the sentence If you are good, then Santa will bring you presents, write: a. The converse: b. The inverse: c. The contrapositive: d. The biconditional: 24) raw a conclusion: -If a student gets an on the final exam, then the student will pass the course. -Felicia gets an on the music theory final exam. 25) raw a conclusion: -If it is a national holiday, then school is not in session. -If school is not in session, then students are at home. 26) Which property of equality or congruence justifies each statement? a. If 3x 14 80, then 3x 66. b. If m 15, then 3m 45. c. If 4m C 100, then m C ) Solve for y. 3y 20 5y 16

5 28) Solve for x. 6x 4 2x 20 29) BC and BC are complementary. What is the m BC if m BC 4x 10 and m BC x 30? 30) If the supplement of T is 47, what is the measure of T?

6 Chapter 3: Parallel and Perpendicular Lines 31) etermine the relationship of the following angles. a. 1 and 2 b. 1 and 6 c. 3 and 6 d. 1 and 7 e. 1 and 5 f. 2 and ) Fill in the blank. a. ngles that form a linear pair. b. ngles that are vertical are. c. Corresponding angles of parallel lines are. d. Same-side interior angles of parallel lines are. e. lternate interior angles of parallel lines are. 33) If m 50, m B 130, m C 50, and they fall on parallel lines cut by a transversal 34) In FUN a. Which angles could be vertical? b. Which angles could be same-side interior? c. Which angles could be alternate interior?, the angles measure 3 x, 2x 20, and 5x 5 smallest angle?, what is the measure of the 35) What is m B? B 30 C 80

7 36) What is the value of x? x 37) What is the value of x? 3x 60 x 20 2x 20 38) If m 60 and m B 60, BC is what kind of triangle? Classify by angles and sides. 39) If m 45 and m B 45, BC is what kind of triangle? Classify by angles and sides. 40) Classify the triangle according to the angle and side length x 41) Find the missing angle measure. a. y b n 6 n ) Find the sum of the measures of each polygon. a. odecagon b. nonagon 43) Find the measure of an interior angle and an exterior angle of each regular polygon. a. Pentagon b. 18-gon

8 44) Find the slope of the line passing through the following points: a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8) 45) Find the slope of the line parallel to the line passing through the following points: a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8) 46) Find the slope of the line perpendicular to the line passing through the following points: a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8) 47) etermine which line is perpendicular to 2 y x 6. 3 a. 2 y x 7 b. 3 3 y x 5 c. 2 3 y x 8 d. 2 2 y x ) etermine which line is parallel to y 4x 3. a. 1 y x 7 b. 4 1 y x 5 c. y 4x 8 d. y 4x ) How can you determine if two lines are parallel? 50) How can you determine if two lines are perpendicular? 51) How can you determine if two lines intersect, but are not perpendicular? 52) Given BC, find m B C B

9 130 53) Given: l m, find x. l 2x 10 m

10 Chapter 4: Congruent Triangles 54) Given that IMP OGR, name all of the pairs of corresponding parts. 55) For each figure below, state the parts you would need to know are congruent in order to prove the triangles congruent by the method stated. O a. SS M b. S I B G T C T c. HL R d. S U S M T P 56) Use the given information to make a conclusion about each figure. U a. I) Y is the midpoint of R M II) UY R III) UY bisects RU R Y b. I) QU II) What parts are congruent just by the picture? Q U

11 JO J 57) Given: ON N Prove: JON N O R N J 58) Given: T is the midpoint of GF GTI FTI Prove: G F I G T F 59) Given: SL CL S U S U SC SU SL is isosceles with base L C L Prove: SCL SU

12 60) is the midpoint of LU C S CL 2x 14 SU 3x 24 C x 10 L U Find the measure of S. 61) Find x 20 x 62) TP is isosceles with vertex angle t. Find m. P 55 T 63) N is isosceles with base. 4x 12 x 33 Find m N 64) BC is isosceles with as the vertex angle. If m B 3x 4, m C 5x 8. Find m B

13 Chapter 5: Relationships within Triangles 65) In MLK, MK is 20in. long. What is its midsegment? 66) Solve for x. 2x ) Solve for y. 3y 6 7y 5 68) a. If F 24, BC 6, and B 8, what is the perimeter of EBC? b. If the perimeter of BCE is 17, what is the perimeter of F? B C E F 69) LJ bisects KLM, find x, JK, and JM. x 5 K J 2x 7 M L

14 70) B is a median. C = 18, B = x-6. Solve for x. C B 71) G is the centroid E a. If G = 7, what is G? b. If GC = 12, what is CF? c. If EB = 48, what is GB? F G B C 72) In FUN, UN 10 cm, UF 16 cm, and FN 14cm. Which angle is the smallest? 73) In HT, 47, T 93. List the sides in order from least to greatest. 74) Could the following be lengths of a triangle? a. 5, 9, 13 b. 7, 14, 20 c. 1, 5, 7 d. 2, 2, 3 75) If one side of a triangle is 17 cm and the second side is 39 cm, what are the possible side lengths for the third side?

15 nswers: 1) 3, 0, -3 2) Point 3) Line 4) C,, E 5) X = 5, BC 11, C 22 6) Midpoint: -4.5, istance: 21 7) X = 13 8) ) B) 3 3, ) ) ) 11 19) C B) 3 3, ) I) 8 cm IB) 32 cm II) 2 16 cm IIB) cm B) 21) h = 6 ft C) ) ) b = 6 cm 23) a) If Santa brings you presents, then you were good b) If you are not good, then Santa will not bring you presents c) If Santa does not bring you presents, then you were not good d) Santa will bring you presents if and only if you are good 24) Felicia will pass the course 9) X = 12, m TSW 50 10) X = 19.5, m RQS ) X = 31 12) X = 11, TO 34 13) 14) X = 12, m GEO 82 15) X = 10, m GIT 35 16) ) ) If it is a national holiday, then students are at home 26) a) Subtraction property of equality 27) y = 18 b) Multiplication property of equality c) ivision property of equality d) Symmetric property of congruence 28) x = 6

16 29) x = 14, m BC 44 30) m T ) a) Supplementary angles 42) a) 1800 b) ) a) interior = 108, exterior = 72 b) interior = 160, exterior = 20 b) lternate interior angles c) Corresponding angles d) Corresponding angles e) Same-side interior angles f) Vertical angles 32) a) are supplementary b) Congruent 44) a) m = 2 b) 45) a) m = 2 b) 1 46) a) m b) 2 47) C 48) 17 m 9 17 m 9 9 m 17 c) Congruent d) Supplementary e) Congruent 33) a), C b), B, and C, B c), C 34) x = 15,5, smallest angle = ) m B ) x 70 37) x = 50 38) Equiangular and equilateral 39) Right and isosceles 40) cute and scalene 41) a) y 102 b) n = 113, n+6=119 49) If the slopes are the same 50) If the slope are opposite reciprocals 51) The slopes are different by not opposite reciprocals 52) m B 40 53) x = 20 54) I O, M G, P R IM OG, MP GR, IP OR 55) ) BI M B) T G C) RM RS ) MUP PU 56) I) RY Y II) m UY m UYR 90 III) RUY UY

17 BI) Q UQ BII) Q Q reflexive property 57) Statement Reason JO J Given ON N Given ONJ N Vertical angles JON N S 58) Statement Reason T is the midpoint of GF Given GTI FTI Given TI TI Reflexive GTI FTI SS 65) 10 in 66) x = 23 67) y = 7 68) a) 52 units b) 34 units 69) x = 12, JK = 17, JM = 17 70) x = 15 71) a) 14 b) 18 c) 16 72) F 73) T, HT, H 74) a) yes b) yes c) no d) yes 75) 22 x 56 G F CPCTC 59) Statement Reason SL CL Given S U Given SC SU Given SL is isosceles Given SCL SU HL 60) x = 38, S = 28 61) x 80 62) m ) x = 15, m 48 64) x = 6, m B 22