Smart s Mill Middle School

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1 Smart s Mill Middle School Geometry Semester Exam Review 0 03 You must show your work to receive credit! Mrs. nderson and Mrs. ox note to remember, for this review N the actual exam: It is always helpful to draw a picture. I encourage you to do that for any problem a picture is not given. GOO LUK. Name: ate: Period: 8 th Geometry Semester Exam Review

2 Part I. Fill in the blank.. line segment contains.. If M = M and points, M and are collinear, then. 3. In a triangle, the smallest angle is (where?). 4. If two parallel lines are cut by a transversal, all corresponding angles are. 5. If is between and and are collinear, then. 6. right triangle has (what types of angels?) and. 7.,,,, (5) are methods to prove triangles congruent. 8. The intersection of two planes is a. 9. In quadrant, the x and y coordinates are both negative. 0. cute angles measure.. Equiangular triangles are also.. Parallel lines have the same. 3. The intersection of two lines is a. 4. If two angles are supplements of congruent angles, then the two angles are. 5. orresponding sides of congruent triangles are. 6. Skew lines are and. 7. The slope of a horizontal line is. 8. Two angles are complementary if. 9. The angles in a triangle sum to. 0. Vertical angles are.. n isosceles triangle has and.. n equilateral triangle has and. 3. If a conditional statement is false, then so is its. 4. The hypotenuse of a right triangle is opposite the. 5. If two sides of a triangle have length 4and 6 then the third side must be. 6. (n) of a right triangle is the longest side. 7. The slope of a vertical line is. 8. In a triangle, the largest angle is. 9. Two lines that are not parallel or skew are. 30. The three medians of a triangle intersect and. 3. When two parallel lines are cut by a transversal, the exterior angles are or. 3. If two lines are parallel, then alternate interior angles are. Geometry Semester Exam Review

3 True or false. hapter Part II. Free response by chapter.. Points, and H are collinear. 4. Points E, J and F are collinear.. Point lies on line m. 5. Point lines on line l. E J F 3. Points, and H are coplanar. 6. Plane and plane F intersect at point. G I H m l For questions 7, refer to the diagram at the right. 7. Name the intersection of and plane P. 8. If T and T were drawn, what would be their intersection? 9. Name the intersection of line l and. 0. Name four noncoplanar points.. Write another name for plane P. P T l For questions, write the following using symbols. o not draw.. a. perpendicular d. parallel g. ray KL a. line segment e. the length of line segment b. angle EFG f. the measure of angle HIJ 3. Find the length of the segment with endpoints H(, 3) and J(6, 7). 4. Find the midpoint of the segment MN with endpoints M(8, 9) and N(-, ). For questions 5 7, determine whether each statement is true of false. 5. If is between M and T, M = T MT. 6. If is the midpoint of T, then T = T. 7. Every segment has only one bisector. 8. If m = 4( m ), find m. 9. Find m if bisects, m = 5x and m = 3x + 5. For questions 0 3, refer to the figure at the right. 0. Name two right angles.. Name two supplementary angles... Name two congruent angles that are not right angles.. 3. Name the obtuse angle The measure of an angle is three times the measure of its supplement. Find the measure of the angle. 5. Find the value of y. 3y+ y+ 6. Find m if m = 75 and m = Find the value of x if m = 6x, m = x+ 5, and m = 3x. Geometry Semester Exam Review 3

4 hapter For questions - 3, determine if the conclusion is true or false based on the given information.. Given: and are adjacent angles. and are opposite rays. onjecture: and are supplements.. Given: PQ PR. onjecture: RPQ is a right angle. 3. Given: J, K and L are collinear. onjecture: JK + KL = JL. For questions 4-6, write the statement in if-then form. Underline the hypothesis once, conclusion twice. 4. Two lines intersect exactly one point. 5. ll tigers are cats. 6. ll right angles measure 90 degrees. Write the converse, inverse and contrapositive of the conditional statement. 7. Vertical angles are congruent. onverse: Inverse: ontrapositive: omplete the following statements. 8. plane contains. 9. line contains. If possible, write the conclusion. State the law of logic that you used, or write no conclusion. 0. a) If you have a driver s license, then you may drive a car. b) indy has a driver s license. c). a) If, then. b) If, then =. c). a) ll right angles are congruent. b) Vertical angles are congruent. c) For questions 3 5, name the property of equality that justifies each statement. 3. If m + m = 80 and m = 0, then 0 + m = If =, then =. 5. If m K = m L, then m K = m L. 6. In the conditional If p, then q, the q is called the. 3x+6 7. Find the measure of. 5x-8 Geometry Semester Exam Review 4

5 hapter 3. How many pairs of skew lines does the figure at the right have? P Refer to the figure below. State the transversal that forms each pair of angles. Then identify the special angle pair name and 7 m 3. and and and and If m = 80, m = 40, and l m, find the angle measures. m =. m 3 =, m 4 =, m 5 =, m 6 =, m 7 =, m 8 =, m 9 =, m 0 =, l y 4 I Find the value of x and y. 8. l m 9. 4 y- 35 3x+ 3y+ l m x- 8 Find the value of x so that p q. 0.. x- x Tell whether a line whose slope is undefined is horizontal, vertical or neither. 3. Find the slope of the line passing through (-3, 0) and (, -). 4. Find the slope of a line parallel to the line passing through (5, -3) and (8, ). 5. Find the slope of the line perpendicular to the line passing through (4, -3) and (, -). 6. Write the equation of the line with a slope of 4 passing through (-, 3). 7. Write the equation of the line parallel to y = x+ 9 passing through (-, 3). 8. Write the equation of the line perpendicular to y = x+ passing through (, 4). 3 Geometry Semester Exam Review 5

6 hapter 4 etermine whether each statement is true or false.. ll isosceles triangles are acute.. n acute triangle can be equilateral. 3. scalene triangle is never obtuse. 4. right triangle can be isosceles. Use the given conditions to classify each triangle by its sides and by its angles. 5. ΔWHO, with m W = 0, WH = WO = 5 cm. 6. ΔG, with m = 90, G = 4 cm, = 3 cm. Find the value of x. 4x x+5 7x+ 7 Write a congruence statement for the congruent triangles in each diagram. Z M R Y J X K P Q L N etermine which postulate or theorem can be used to prove the triangles congruent... M 3. J K lways, sometimes or never. 3. n equilateral triangle is an isosceles triangle. 4. n isosceles triangle is an equilateral triangle. 5. triangle has one obtuse angle and one right angle. 6. n equilateral triangle is an obtuse triangle. 7. n equilateral triangle is an acute triangle. L N E 70 Find the value of x and y. y x 4 4. What is the vertex for? Geometry Semester Exam Review 6 49 X y x

7 hapter 5. Name the triangle for which G is a median.. Name an altitude of ΔG. 3. Name a median to G in ΔG. E F 4. Name a perpendicular bisector to triangle. G 5. Name an angle bisector. to angle. List the sides of ΔWXY in order from longest to shortest if the angles of ΔWXY have the indicated measures. 6. m W = 4x m X = 7x + 3 m Y = 3x 4 7. m W = 5x + m X = 6x - 5 m Y = 48 x 8. Two sides of a triangle are 6 and centimeters in length. etermine whether 39 centimeters can be the length of the third side? 9. Two sides of a triangle are and 4 centimeters in length. etermine whether 40 centimeters can be the length of the third side? Write the inequality relating each pair of measures. 0. m PRQ m PRS. m m E 7 R 5 5 Q E 6 P 9 S Write an inequality to describe the possible values of x. 0 R. 3. Q x+ 4x- 5 x- 55 P 5 S 3x- Geometry Semester Exam Review 7

8 Part III: Multiple hoice hoose the best answer for each question. hapter. Find the length of the segment with endpoints L(-, -3) and M(-6, 9) Points, and. determine a plane. are collinear. are contained in only plane P. are noncoplanar points 3. What is the intersection of planes P and R. points, and... R F G E P 4. What is the measure of QT if R is between Q and T, QR = 4 and RT = 5? Find the coordinates of the midpoint of the segment with endpoints (6, 6) and E(-, ).. (3, 4). (, 4). (4, 8). (, -) 6. What are the sides of 5?. W and WF. and WF. W and WG. WF and WG 7. 5 and 6 are. adjacent. vertical. supplementary. complementary 8. 8 and 9 are. adjacent. vertical. supplementary. complementary 9. and are. adjacent. vertical. complementary. linear pair 0. 3 and 4 are. adjacent. vertical. linear pair. complementary 8 E W 5 6 G F. Find m x+ x+. If m = 40 and m = 0, find m Find m RSU if ST bisects RSU, m = 4x and m = x hapter Geometry Semester Exam Review 8 S R T U

9 . hoose the converse of If, then m = m.. If m = m, then. If, then. If m = m, then m = m.. None of these. Identify the hypothesis of the statement If today is Tuesday, then tomorrow is Wednesday.. Today is not Tuesday. Today is Wednesday. Today is Tuesday. Tomorrow is Wednesday 3. Identify the if-then form of the following: ll cars have four wheels.. If a vehicle has four wheels, then it is a car.. If a vehicle is a car, then it has four wheels.. If a vehicle is not a car, then it does not have four wheels.. None of these 4. hoose the statement that follows () and () by the law of detachment. () Right angles are congruent. () and are right angles. m = 90. m = 90.. m = m 5. Which statement represents the law of syllogism.. If p q is a true conditional and p is true, then q is true.. If p q and q rare true conditionals, then p r is true.. If a, b and c are real numbers, then a(b + c) = ab + ac.. None of these 6. The transitive property of equality states If a = b and b = c, then.. b = a. a = c. c = b. b = b 7. P and Q form a linear pair and m P = 6. Find m Q Geometry Semester Exam Review 9

10 hapter 3. Given l m and m = 7, find m Given l m, m = 9x +5 and m = x + 37, find the value of x Given m 4= 5x+ and m 5 = 3x + 8, find the value of x so that l m m l hapter 4. right triangle must be. isosceles. acute. scalene. either isosceles or scalene. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x 7 and PR = x In Δ, what is the angle opposite? In Δ EF, if E F and EF is the hypotenuse, then ΔEF is. acute and scalene. right and scalene. right and isosceles. obtuse and isosceles 5. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle? If ΔIGH ΔKLJ, then H is congruent to. J. I. K. L 7. Which of the following is not a postulate used to prove the congruence of two triangles?. S. SS. SS. SSS 8. The measure of the vertex angle of an isosceles triangle is 0. That is the measure of the base angle? Name one additional pair of corresponding parts that need to be congruent in order to prove that Δ STP ΔMKO by S. T K. S M. TP KO. T K. ST MK S P M O Geometry Semester Exam Review 0

11 . Identify the median of Δ.. E. F.. GH. Identify the altitude of Δ.. E F.. GH hapter 5 F G 3. In Δ, if m F = 39 and F is an angle bisector, find m E H E 4. What is the longest side of the figure QU.. Q QU. U. Q U 5. In ΔEFG, m E= 6x 8, m F = 7x + 3, and m G = 3x 7. hoose the list that shows the sides correctly ordered from shortest to longest.. EF, FG, EG. FE, EG, GF. EG, GF, FE. GF, EG, FE 6. etermine which set of numbers can be the measures of the sides of a triangle.. 3, 0, 6.,, 3. 5.,, , 9, 9 7. Two sides of a triangle have lengths 5 cm and 9 cm. Which measurement can be the length of the third side?. 6 cm. 4 cm. 40 cm. 36 cm 8. If the sides of a triangle have measures 3x + 4, 6x and 8x +, find all possible values of x x > -. x >. x >. x > If M is the midpoint of JK, m > m, JL = 0x +, and LK = 6x + 4, which is a possible value of x?.. K J L Geometry Semester Exam Review

12 Properties State the property, theorem, postulate or definition used to make the conclusion.. If UV = VW, then VW = UV.. If Q is a right angle, then m Qis (x 50) = x If and are vertical angles, then. u 5. If t u, then is a right angle =. 7. If, then m = m If x + 4 = 7, then x = T is the midpoint of SR, then ST TR.. If and 3, then 3.. If 3 and 4 are a linear pair, then they are supplementary. 3. If bisects, then. 4. If 4 and 5 are supplementary, then m 4 + m 5 = If l m, then m + m = , then l m. t 3 l 4 m Geometry Semester Exam Review

13 Proofs R. Given: RF T Prove: Δ FR ΔTFR F is a midpoint of T Statements Reasons F T E. Given: E Prove: Δ E Δ E Statements Reasons Given: W is a midpoint of ZX Prove: ZV YX VW WY Statements Z Reasons V W Y X Geometry Semester Exam Review 3

14 4. Given: 3(x 5) + = (x 3) Prove: x = Statements Reasons Given: a b 4 c d a Prove: c d 3 4 b Statements Reasons. a b c d 6. Geometry Semester Exam Review 4