SHELBY COUNTY SCHOOLS: GEOMETRY 1ST NINE WEEKS OCTOBER 2015

Transcription

1 SHELBY COUNTY SCHOOLS: GEOMETRY 1ST NINE WEEKS OCTOBER 2015 Created to be taken with the ACT Quality Core Reference Sheet: Geometry. 1 P a g e

2 1. Which of the following is another way to name 1? A. A B. AYZ C. ZYA D. YAZ W X A 1 Z Y 2. By definition, which of the following properties do all perpendicular lines have? A. Do not intersect to form angles B. Form four acute angles C. Form four right angles D. Form four obtuse angles 3. Given the definition of circle, which pair of points consists of two points not in the locus of points equidistant from the center of Circle O? A. A and C B. B and D C. C and D D. A and B A D O B C Definition of Circle: The locus of all points in a plane equidistant from a given point called the center of the circle. 4. Which of the following words best describes the following: the intersection of two noncollinear rays at a common endpoint? A. Ray B. Line Segment C. Line D. Angle 5. By definition, parallel lines have which one of the following properties? A. Vertical B. Noncoplanar C. Intersecting D. Coplanar 2 P a g e

3 6. Which of the following angles is adjacent to LNP? L M A. MNO B. QNM C. PNQ D. None of the above P N O Q 7. What theorem justifies that 6 and 7 are congruent? A. Complement Theorem B. Perpendicular Theorem C. Supplement Theorem D. Vertical Angles Theorem 8. What theorem justifies that m NOQ + m QOP = 90? A. Supplement Theorem B. Complement Theorem C. Vertical Angles Theorem D. Perpendicular Theorem 9. Write the reason for the missing part of the proof. Given: 1 and 2 form a linear pair 2 and 3 are supplementary Prove: 1 3 Statements 1. 1 and 2 form a linear pair 1. Given Reasons 2 and 3 are supplementary 2. 1 and 2 are supplementary Supplement Theorem 3.? A. Angles complementary to the same angle or to congruent are congruent B. Angles supplementary to the same angle or to congruent angles are congruent C. Definition of congruent angles D. Supplement Theorem 3 P a g e

4 10. Find y so that l m. Identify the postulate or theorem you used. A. 25; Consecutive Interior Angles B. 25; Alternate Interior Angles C. 12; Alternate Exterior Angles D. 12; Corresponding Angles 11. Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. Given: CBF DCG A. BF B. BF C. BD D. BD CG CG ; Converse Corresponding Angles Theorem ; Converse Consecutive Interior Angles Theorem EG ; Converse Corresponding Angles Theorem EG ; Converse Consecutive Interior Angles Theorem 12. What is the missing reason in the two-column proof? Given: 2 and 3 are supplementary Prove: AB CD Statements 1. 2 and 3 are supplementary 2. AB CD 3. AB CD 1. Given 2.? Reasons 3. Segments contained in parallel lines are parallel. A. If alternate interior angles are supplementary, then lines are parallel. B. If consecutive interior angles are congruent, then lines are parallel. C. If consecutive interior angles are supplementary, then lines are parallel. D. If corresponding angles are supplementary, then the lines are parallel. 4 P a g e

5 13. Which of the following is a construction of a perpendicular bisector? A. C. B. D. 14. Which of the following equations represents a line that is perpendicular to the line with the equation y = 2 3 x + 3? A. y = 2 x 8 3 B. y = 3 x 1 2 C. y = 2 x 5 3 D. y = 3 x Which of the following equations represents a line that is parallel to y = 1 x + 2 and passes through the point 4 (4, 1)? A. y = 1 x B. y = 1 4 x 2 C. y = 1 4 x 1 D. y = 4x Line q has a slope of 5 and passes through the point (0, 3). What is the equation of a line that is parallel to line q and passes through the point (1, 3)? A. y = 5x + 8 B. y = 5x 8 C. y = 5x + 3 D. y = 5x 3 5 P a g e

6 17. Line t has an equation of 2x + 4y = 8. Line t is perpendicular to line s. Lines s and t intersect on the y-axis. What is the equation of line s? A. y = 2x + 2 B. y = 2x + 2 C. y = 1 2 x + 2 D. y = 1 2 x The equation of line a is 2x + y = 4 and the equation of line b is 3x + 6y = 12. Determine the relationship between the two lines. A. Coinciding B. Intersecting C. Intersecting and perpendicular D. Parallel 19. Which of the following equations represents a line that is perpendicular to 2x y = 5 and passes through the point (4, 2)? A. y = 1 x 2 B. y = 1 x 2 C. y = 1 x D. y = 1 x Identify the shape you would see if you cut a cube in half horizontally. A. Triangle B. Circle C. Square D. Trapezoid 21. Identify the shape you would see if you cut the following shape in half vertically. A. Triangle B. Rectangle C. Circle D. Trapezoid 6 P a g e

7 22. The Louvre has a glass structure that serves as its entrance. The structure has a square base that is 35 meters on each side and triangular faces that come to a point 21.6 meters high. Into what group of geometric shapes can the Louvre s main entrance be categorized? A. Cones B. Prisms C. Pyramids D. Spheres 23. While sitting in class, you look up and notice the ceiling tiles. Each tile has four right angles, measures 2 x 2, and, with a little investigating, are determined to be 1 thick. What is the most specific name for the geometric shape of the ceiling tile? A. Cube B. Rectangular Prism C. Square Prism D. Triangular Prism 24. A blueprint of a building has a steel truss with endpoints at (5, 2) and (8, 2). The architect wants to add one more support beam to a point at (6, 4) on the truss to make it more stable. To minimize costs, what is the shortest length the beam can be? A. 2 units B. 3 units C. 4 units D. 5 units 7 P a g e