Download Geometry Semester 1 Exam 1. A bisector of !AB contains which line

Geometry Semester 1 Exam 1. A bisector of !AB contains which line segment? A. !CG B. !DF C. !DG D. !EF 2. In the figure, line l is parallel to line m. Which of the following pairs of angles must have the same measure? A. Angles 1 and 2 B. Angles 1 and 5 C. Angles 2 and 3 D. Angles 4 and 5 E. Angles 4 and 8 3. In this figure, transversal e intersects lines a, b, c, and d. Which lines must be parallel? A. a and c B. b and c C. b and d D. a and d 4. In the figure shown, line q is a transversal of parallel lines l, m, n, and p. What are the values of x and y? A. x=150, y=30 B. x=30, y=150 C. x=30, y=30 D. x=150, y=150 5. Lines k, l, and m are three different lines. If line k is parallel to line l and line l is parallel to line m, which of the following statements must be true? A. Line k is perpendicular to line l. B. Line k is perpendicular to line m. C. Line k is parallel to line m. D. Line k intersects line l. E. Line k intersects line m. 6. In the figure shown, m∠1=(4x+12)° and m∠2=(6x+8)°. What is m∠1 ? A. 7° B. 20° C. 40° D. 50° E. 76° 7. Given: In this figure, !AC and !BD bisect each other. Based on the information given, which triangle congruence theorem could be used to prove ΔAED !ΔCEB? A. Angle-­‐Angle-­‐Side (AAS) B. Angle-­‐Side-­‐Angle (ASA) C. Side-­‐Angle-­‐Side (SAS) D. Side-­‐Side-­‐Side (SSS) 8. In the figure shown, what is m∠WXY? A. 45° B. 107° C. 120° D. 135° 9. In the diagram, m∠1=(6x+12)° and m∠2=(9x−4)°. Which is closest to the value of x ? A. 5.3 B. 5.5 C. 11.5 D. 12.5 10. In parallelogram ABCD, what is m∠C? A. 60° B. 82.5° D. 120.0° E. 130.0° C. 97.5° 11. Which statement is true about the side lengths of ΔABC? A. BC > AC > AB B. AB > AC > BC C. AC > AB > BC D. BC > AB > AC 12. Which figure has all sides of equal measure but not necessarily all angles of equal measure? A. Square B. Rectangle C. Rhombus D. Trapezoid 13. In each of the following figures, transversal c cuts lines a and b. In which figure are ∠1 and ∠2 corresponding angles? A. B. C. D. 14. With the information given in the drawings, which pair of triangles can be proven congruent by the Side-­‐Angle-­‐Side postulate? A. B. C. D. 15. Jake took pictures of Ana’s flag while she was practicing her routine for the football game, as shown below. Which of the following best describes the movement of the flag from picture to picture? A. Reflection, rotation, translation B. Rotation, translation, translation C. Rotation, translation, dilation D. Reflection, translation, translation 16. Lines m and r are cut by a transversal. What value of x will show that line m is parallel to line r ? A. 20 B. 24 C. 25 D. 33 17. For what measure of ∠D is !AB P DC in this figure? A. 26° B. 59° C. 69° D. 85° E. 95° 18. This figure represents line segments painted on a parking lot to create parking spaces. Which equation can be used to show that these line segments are parallel? A. w+118=180 B. x+118=180 C. 118−x=w D. 118−w=x 19. Use the proof to answer the question below. Given: ∠2≅∠3 Prove: ∠1≅∠4 Statements Reasons 1. ∠2≅∠3 1. Given 2. ∠1≅∠2; ∠3≅∠4 2. ? 3. ∠1≅∠4 3. Transitive Property of Congruence What reason can be used to justify statement 2? A. Complements of congruent angles are congruent. B. Vertical angles are congruent. C. Supplements of congruent angles are congruent. D. Corresponding angles are congruent. 20. In the figure below, n is a whole number. What is the smallest possible value for n? A. 1 B. 7 C. 8 D. 14 21. John wants to make a triangular garden. Which of the following are possible dimensions? A. 4 ft by 5 ft by 10 ft B. 6 ft by 6 ft by 12 ft C. 6 ft by 8 ft by 10 ft D. 8 ft by 12 ft by 20 ft 22. A trapezoid is located entirely in quadrant II. If this trapezoid is reflected across the x-­‐axis, in which quadrant will the new trapezoid be located? A. I B. II C. III D. IV 23. Statement: If lines are skew, then they are not coplanar. What is the contrapositive of the statement? A. If lines are not coplanar, then they are not skew. B. If lines are not skew, then they are coplanar. C. If lines are coplanar, then they are not skew. D. If lines are skew, then they are coplanar. 24. Consider the following statement. If 4x=8, then x=2. Which is the inverse of the statement? Note: ≠ is the symbol for “is not equal to”. A. If x=2, then 4x=8. B. If x≠2, then 4x≠8. C. If x=2, then 4x≠8. D. If 4x≠8, then x≠2. 25. Two angles of a triangle have measures of 55° and 65°. Which of the following could not be a measure of an exterior angle of the triangle? A. 115° B. 120° C. 125° D. 130° 26. The sum of the interior angles of a polygon is the same as the sum of its exterior angles. What type of polygon is it? A. quadrilateral B. hexagon C. octagon D. decagon 27. What is m∠1? A. 34° B. 54° C. 56° D. 64° E. 92° 28. What is the value of x? 29. What is the value of y? 30. What is the value of z? 31. What is the value of m? 32. ΔPQR has vertices P(−1,3), Q(1,2), and R(−2,−1). When ΔPQR is reflected over the line y=−2, what are the coordinates of P’? A. (−1,−3) B. (−1,−7) C. (−2,−2) D. (−3,−3) 33. If triangle ABC is rotated 180 degrees about the origin, what are the coordinates of Aʹ′? A. (−5,−4) B. (−5,4) C. (−4,5) D. (−4,−5) 34. Trapezoid ABCD is to be translated to trapezoid A’B’C’D’ by the following motion rule: (x,y) → (x+3,y−4). What are the coordinates of D’? A. (1,−3) B. (2,1) C. (6,1) D. (8,−3) 35. ΔPQR, shown below, will be rotated clockwise 180° about the origin. Which rule describes the transformation? A. (x’,y’)=(x,y) B. (x’,y’)=(−x,y) C. (x’,y’)=(x,−y) D. (x’,y’)=(−x,−y) 36. In the graph, ΔP’Q’R’ is the image produced by applying a transformation to ΔPQR. Which rule describes the transformation? A. (x’,y’)=(x,y) B. (x’,y’)=(−x,−y) C. (x’,y’)=(−x,y) D. (x’,y’)=(x,−y) 37. Which expression describes the translation of a point from (−3,4) to (4,−1)? A. 7 units left and 5 units up B. 7 units right and 5 units up C. 7 units left and 5 units down D. 7 units right and 5 units down 38. Point P’ is the image of point P after a counterclockwise rotation of 90° about the origin. If the coordinates of point P’ are (−7,3), what are the coordinates of point P? A. (−3,−7) B. (−3,7) C. (3,−7) D. (3,7) 39. A translation is applied to ΔFGH, forming ΔFʹ′Gʹ′Hʹ′. If the translation is described by (xʹ′,yʹ′) → (x+2,y−3), which graph shows the translation correctly? A. B. C. D. 40. Given ∠VYX is bisected by ray YW, m∠VYX=(6r−18), and ∠VYW=36. What is the value of r? A. 9 B. 15 C. 30 D. 36 41. What geometric construction is shown in the diagram below. A. an angle bisector B. a line parallel to a given line C. an angle congruent to a given angle D. a perpendicular bisector of a segment E. 72 42. Given: angle A What is the first step in constructing the angle bisector of angle A? A. Draw ray AD. B. Draw a line segment connecting points B and C. C. From points B and C, draw equal arcs that intersect at D. D. From point A, draw an arc that intersects the sides of the angle at points B and C. 43. Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing? A. a line through P parallel to line l B. a line through P intersecting line l C. a line through P congruent to line l D. a line through P perpendicular to line l 44. Which set of statements represents a valid deductive argument? A. All quadrilaterals have 4 angles. All parallelograms have 4 angles. All quadrilaterals are parallelograms. B. All parallelograms have diagonals that bisect each other. All parallelograms have opposite sides that are parallel. All polygons whose diagonals bisect each other have opposite sides that are parallel. C. All rectangles have 4 right angles. All squares have 4 right angles. All rectangles are squares. D. All parallelograms have 4 sides. All polygons with 4 sides are quadrilaterals. All parallelograms are quadrilaterals. 45. This figure shows a pattern of triangles and regular hexagons. What is the value of x? A. 30 B. 60 C. 90 D. 120 46. Figure 1 is a regular hexagon with its center at point P. The dotted lines divide the hexagon completely into 6 congruent triangles sharing a vertex at point P. Figure 2 is a regular octagon with its center at point Q. The octagon can be completely divided into congruent triangles sharing a vertex at point Q. This division could produce A. sixteen congruent equilateral triangles. B. sixteen congruent isosceles triangles. C. eight congruent right triangles. D. eight congruent equilateral triangles. E. eight congruent isosceles triangles 47. You will need one piece labeled X, one piece labeled T, and one piece labeled R to answer this question. Which of the pieces has an angle greater than a right angle? A. Only X B. Only R C. Only T D. Both R and T 48. A geometry student concluded: If two sides and a non-­‐included angle of one triangle are congruent to two sides and a non-­‐included angle of another triangle, then the two triangles are congruent. Which diagram can be used as a counterexample to the student’s conclusion? A. B. C. D. 49. Which Venn diagram represents all the following set of statements? • Some triangles are acute. • Some triangles are obtuse. • No triangle is both acute and obtuse. • Some acute triangles are equilateral. A. B. C. D. 50. Let p=An equation is of the form y=mx+b. Let q=Its graph is a line. Argument: If an equation is of the form y=mx+b, then its graph is a line. The graph is not a line. Therefore, the equation is not of the form y=mx+b. Which of the following is the symbolic representation of the given argument? Note: ∴ is the symbol for “therefore”. A. B. C. D. 51. Which triangles must be similar? A. two obtuse triangles B. two scalene triangles with congruent bases C. two right triangles D. two isosceles triangles with congruent vertex angles 52. The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between the areas of the two squares? A. 2 to 3 B. 4 to 9 C. 16 to 27 D. 16 to 81 AB BC
53. If ΔABC and ΔXYZ are two triangles such that , which of the following would be sufficient to prove the =
! XY YZ
triangles are similar? A. ∠A≅∠X B. ∠B≅∠Y C. ∠C≅∠Z D. ∠X≅∠Y 54. Given: ΔABC∼ΔLMN. What is the length of !AC ? A. 11 B. 12 C. 22 D. 24 55. Which of the following facts would be sufficient to prove that triangles ABC and DBE are similar? A. !CE and !BE are congruent. B. ∠ACE is a right angle. C. !AC and !DE are parallel. D. ∠A and ∠B are congruent. 56. Triangle RST was dilated to create triangle Rʹ′Sʹ′Tʹ′, as shown on the coordinate grid below. Which statement appears to be true? A. The center of dilation used to create ΔRʹ′Sʹ′Tʹ′ was (−10, 8). B. ΔRST and ΔRʹ′Sʹ′Tʹ′ are congruent. C. The scale factor used to create ΔRʹ′Sʹ′T ʹ′ is 2.5. D. ΔRST was reduced in size to create ΔRʹ′Sʹ′T ʹ′. 57. A company packages their product in two sizes of cylinders. Each dimension of the larger cylinder is twice the size of the corresponding dimension of the smaller cylinder. Based on this information, which of the following statements is true? A. The volume of the larger cylinder is 2 times the volume of the smaller cylinder. B. The volume of the larger cylinder is 4 times the volume of the smaller cylinder. C. The volume of the larger cylinder is 8 times the volume of the smaller cylinder. D. The volume of the larger cylinder is 6 times the volume of the smaller cylinder. ⎡
⎤
58. The vertex matrix for ΔPQR is ⎢ −2 2 3 ⎥ . The graph −2 4 −3 ⎦
!⎣
shows ΔPQR and its image, ΔPʹ′Qʹ′Rʹ′, after a transformation. Which matrix expression produces the vertex matrix for ΔPʹ′Qʹ′Rʹ′? ⎤
⎡
⎤
1⎡
A. ⎢ −2 2 3 ⎥ B. 2 ⎢ −2 2 3 ⎥ 2 ⎣ −2 4 −3 ⎦
−2 4 −3 ⎦
!
! ⎣
⎤
⎡
⎤
1⎡
C. ⎢ −4 4 6 ⎥ D. 2 ⎢ −4 4 6 ⎥ 2 −4 8 −6 ⎦
−4 8 −6 ⎦
! ⎣
! ⎣
59. Which drawing contains a pair of similar triangles? A. B. C. D. ⎡
⎤
60. The vertex matrix for ΔJKL is ⎢ −2 2 4 ⎥ . ΔJKL is translated 2 units right and 3 units up, resulting in ΔJʹ′Kʹ′Lʹ′. A 1
5
3
⎦
!⎣
translation of 4 units left and 1 unit up is applied to ΔJʹ′Kʹ′Lʹ′, resulting in ΔJʹ′ʹ′Kʹ′ʹ′Lʹ′ʹ′. Which matrix expression gives the vertex matrix for ΔJʹ′ʹ′Kʹ′ʹ′Lʹ′ʹ′? ⎡
⎤ ⎡
⎤
⎡
⎤ ⎡
⎤
A. ⎢ −2 2 4 ⎥ + ⎢ 2 2 2 ⎥ B. ⎢ −2 2 4 ⎥ + ⎢ −4 −4 −4 ⎥ 1 5 3 ⎦ ⎣ 3 3 3 ⎦
1 5 3 ⎦ ⎣ 1 1 1 ⎦
!⎣
!⎣
⎡
⎤ ⎡
⎤
⎡
⎤ ⎡
⎤
C. ⎢ −2 2 4 ⎥ + ⎢ 2 2 2 ⎥ D. ⎢ −2 2 4 ⎥ + ⎢ −2 −2 −2 ⎥ 1 5 3 ⎦ ⎣ 2 2 2 ⎦
1 5 3 ⎦ ⎣ 4 4 4 ⎦
!⎣
!⎣