3. 4. fraction can not be the length of the third side?

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1 Name: Teacher: Mrs. Ferry 1. 2 In the construction shown below, is drawn If two sides of a triangle have lengths of and, which fraction can not be the length of the third side? In ABC, 2. 3 Given: is the 1. perpendicular bisector of side 2. median to side 3. altitude to side 4. bisector of ACB bisects at C and are drawn ABC EDC 4. 2 Which statement is not always true when ABC XYZ? CAB ZXY 4. BCA YZX 5. 1 In ABC shown below, medians,, and intersect at point R. Which statement is needed to prove ABC EDC using ASA? 1. ABC and EDC are right angles. 2. bisects at C. 3. BCA DCE 4. DEC BAC If CR = 24 and RF = 2x 6, what is the value of x? When the transformation T 2,-1 is performed on point A, its image is point A ( 3, 4). What are the coordinates of A? 1. (5, 5) 3. ( 1,3) 2. ( 5,5) 4. ( 6, 4)

2 7. 3 In ABC, m CAB = 2x and m ACB = x If is extended through point B to point D, m CBD = 5x 50. What is the value of x? Consider triangle ABC graphed below: 8. 3 In the diagram below,. Transversal and line segment HF are drawn. If m HFG = 130 and m EHF = 70, what is m ABE? Triangle ABC will be rotated 90 clockwise around the origin and then reflected across the y-axis. Which additional transformation(s) will map the image triangle back onto the original triangle? As shown in the diagram below of ABC, through D, m A = 70, and m ACD = 115. is extended 1. Rotate 270 clockwise around the origin. 2. Reflect across the line y = x. 3. Reflect across the line y = x, then rotate 180 counterclockwise. 4. Rotate 180 clockwise around the origin. Which statement is true? 1. AC > AB 2. AB > BC 3. BC < AC 4. AC < AB

3 11. 1 In the diagram below, bisects at B, and bisects at C In parallelogram QRST shown below, diagonal and V are points on and, respectively, and intersects at W. is drawn, U Which statement is always true? bisects at C. 4. bisects at B Which transformation would result in the perimeter of a triangle being different from the perimeter of its image? 1. (x,y) (y,x) 2. (x,y) (x, y) 3. (x,y) (4x,4y) 4. (x,y) (x + 2,y 5) If m S = 60, m SRT = 83, and m TWU = 35, what is m WVQ? Which set of numbers could be the lengths of the sides of an isosceles triangle? 1. {1, 1, 2} 3. {3, 4, 5} 2. {3, 3, 5} 4. {4, 4, 9} In ΔABC, m B < m A < m C. Which statement is false? 1. AC > BC 2. BC > AC 3. AC < AB 4. BC < AB What is the measure of each interior angle in a regular octagon? The lengths of two sides of a triangle are 7 and 11. Which inequality represents all possible values for x, the length of the third side of the triangle? 1. 4 x x < < x < x < The sum of the interior angles of a regular polygon is 720. How many sides does the polygon have? In quadrilateral ABCD, each diagonal bisects opposite angles. If m DAB = 70, then ABCD must be a 1. rectangle 3. rhombus 2. trapezoid 4. square

4 20. 1 What are the coordinates of the image of point A (2, -7) under the translation (x, y) (x - 3, y + 5)? 1. (-1, -2) 3. (5, -12) 2. (-1, 2) 4. (5, 12) A sequence of transformations maps rectangle ABCD onto rectangle A B C D, as shown in the diagram below. Which sequence of transformations maps ABCD onto A B C D and then maps A B C D onto A B C D? 1. a reflection followed by a rotation 2. a reflection followed by a translation 3. a translation followed by a rotation 4. a translation followed by a reflection A parallelogram must be a rectangle when its 1. diagonals are perpendicular 2. diagonals are congruent 3. opposite sides are parallel 4. opposite sides are congruent

5 23. 1 Steve drew line segments ABCD, EFG, BF, and CF as shown in the diagram below. Scalene BFC is formed. Which statement will allow Steve to prove? 1. CFG FCB 2. ABF BFC 3. EFB CFB 4. CBF GFC In the diagram below, line is parallel to line m, and line w is a transversal. If m 2 = 3x + 17 and m 3 = 5x - 21, what is m 1?

6 25. 2 A student used a compass and a straightedge to construct in ΔABC as shown below. Which statement must always be true for this construction? 1. CEA CEB 2. ACE BCE In ΔCAT, m C = 65, m A = 40, and B is a point on side, such that. Which line segment is shortest? In ΔFGH, m F = m H, GF = x + 40, HF = 3x 20, and GH = 2x The length of is In the diagram of Δ PQR shown below, is extended to S, m P = 110, m Q = 4x, and m QRS = x 2 + 5x. What is m m Q?

7 29. 1 In the diagram below, point K is in plane P. How many lines can be drawn through K, perpendicular to plane P? an infinite number In the diagram below, ΔXYV ΔTSV. Which statement can not be proven? 1. XVY TVS 2. VYX VUT In the diagram below, bisects RST. Find x, m RSU, m UST and m RST. The value of x is 5. m RSU = 36 m UST = 36 m RST = 72

8 32. If DF = 190, find the value of x. Then find DE and EF. The value of x is 20. DE = 110 EF = Triangle ABC is shown in the diagram below. If joins the midpoints of and, which statement is not true? 1. DE = CB ΔABC ΔAED The diagram below shows the construction of an equilateral triangle. Which statement justifies this construction? 1. A + B + C = m A = m B = m C 3. AB = AC = BC 4. AB + BC > AC

9 35. 1 In the diagram below of ΔABC,,, and. Point P must be the 1. centroid 3. incenter 2. circumcenter 4. orthocenter 36. The coordinates of the vertices of ΔRST are R( 2, 3), S(4, 4), and T(2, 2). Triangle R'S'T' is image of ΔRST after a rotation of 90 about the origin. State the coordinates of the vertices of ΔR'S'T'. [The use of the set of axes below is optional.] Answer: R (-3, -2), S (-4, 4), T (2, 2)

10 37. 4 The diagram below shows a pair of congruent triangles, with ADB CDB and ABD CBD In the accompanying diagram, and. Which statement is true? Which statement must be true? 1. ADB CBD 2. ABC ADC m 1 = m 3 2. m 1 > m 3 3. m 1 + m 2 + m 3 = m 1 + m 2 = m When a quadrilateral is reflected over the line y = x, which geometric relationship is not preserved? 1. congruence 3. parallelism 2. orientation 4. perpendicularity 40. In the accompanying diagram of parallelogram DEFG, m E = 2x + 20 and m F = x Find the number of degrees in the measure of angle G. Answer: m G = 120

11 41. 4 In the diagram below of ΔGJK, H is a point on,, m G = 28, and m GJK = 70. Determine whether ΔGHK is an isosceles triangle and justify your answer. 1. Yes, because angles GKH and KGH are congruent. 2. No, because angles GKH and KHJ are not congruent. 3. Yes, because there are two congruent angles in triangle GHK. 4. No, because there are no two congruent angles in triangle GHK In the diagram of ΔABC shown below, name the intersection of the three lines and the type of line shown in red. 1. Orthocenter, created by the altitudes 2. Incenter, created by the angle bisectors 3. Centroid, created by the medians 4. Circumcenter, created by the perpendicular bisectors Triangle PQR has angles in the ratio of 2:3:5. Which type of triangle is ΔPQR? 1. acute 3. obtuse 2. isosceles 4. right

12 44. 2 Line segment AB is shown in the diagram below. Which two sets of construction marks, labeled I, II, III, and IV, are part of the construction of the perpendicular bisector of line segment AB? 1. I and II 3. II and III 2. I and III 4. II and IV Below is a construction for the angle ABC. What does the construction create? 1. The perpendicular bisector of angle ABC. 2. The angle bisector of angle ABC. 3. The median of angle ABC. 4. The altitude of angle ABC.

13 46. 2 In the diagram below of quadrilateral ABCD with diagonal, m A = 93, m ADB = 43, m C = 3x + 5, m BDC = x + 19, and m DBC = 2x + 6. If is parallel to, find m C The diagram below shows isosceles trapezoid ABCD with and. If m BAD = 2x and m BCD = 3x + 5, find m BAD. Answer: m BAD = 70

14 48. In the diagram below, quadrilateral STAR is a rhombus with diagonals and intersecting at E. ST = 3x + 30, SR = 8x 5, SE = 3z, TE = 5z + 5, AE = 4z 8, m RTA = 5y 2, and m TAS = 9y + 8. Find SR, RT, and m TAS. SR: 51 RT: 90 m TAS: The pentagon in the diagram below is formed by five rays In which quadrant does the image of (4, -7) lie after the translation that shifts (x, y) to (x - 6, y + 3)? 1. I 3. III 2. II 4. IV An exterior angle at the base of an isosceles triangle is always 1. obtuse 2. acute 3. greater than the sum of the base angles 4. equal to the sum of the base angles What is the image of (-2, 5) after a reflection in the origin? 1. (2, 5) 3. (-2, -5) 2. (5, 2) 4. (2, -5) What is the degree measure of angle x? In ΔRST, m R = 58 and m S = 72. Which is the shortest side of the triangle?

15 50. 2 In the diagram, ABCD is a rectangle, E is a point on, m DAE = 30, and m CBE = The measure of the vertex angle of an isosceles triangle is three times the measure of a base angle. Find the number of degrees in the measure of the vertex angle The point R(-2, 5) is reflected in the x-axis. In which quadrant does the image of point R lie? 1. I 3. III 2. II 4. IV What is m x? What is the image of (-4, -5) when reflected in the x-axis? 1. (5, -4) 3. (-4, 5) 2. (-5, -4) 4. (4, -5) 58. Triangle ABC has coordinates A( 1, 3), B( 6, 5), and C( 4, 7). (a) The coordinates of ΔA' B'C', the image of ΔABC after a reflection in the x-axis, are A'(-1, -3), B'(-6, -5), and C'(-4, -7). (b) The coordinates of ΔA'' B''C'', the image of ΔABC after a reflection in the line y = x, are A''(3, -1), B''(5, -6), and C''(7, -4). (c) The coordinates of ΔA''' B'''C''', the image of ΔABC under the translation which maps (x, y) to (x + 8, y + 3), are A'''(7, 6), B'''(2, 8), and C'''(4, 10) If two sides of a triangle have lengths 4 and 9, then the length of the third side may be any number 1. greater than 4 but less than 9 2. greater than 5 3. less than greater than 5 but less than The sum of the measures of the interior angles of a hexagon is