Arkansas Council of Teachers of Mathematics State Contest. Geometry Exam

Transcription

1 rkansas ouncil of Teachers of Mathematics 2013 State ontest Geometry Exam In each of the following choose the EST answer and shade the corresponding letter on the Scantron Sheet. nswer all 25 multiple choice questions before attempting the tie-breaker questions. The tie-breaker questions at the end are to be used to resolve any ties between 1 st, 2 nd, and/or 3 rd place. e sure that your name is printed on each of the tiebreaker pages. The figures are not necessarily drawn to scale. Good Luck! 1. Two lines intersect to form an angle that has a measure of 53 o. nother angle formed by the two lines has a measure of. 180 o. 37 o. 127 o. 137 o 2. n angle is two-thirds its supplement. The complement of the angle is. 72 o. 28 o. 18 o. 108 o 3. The center of a circle is the point (2, -3). The circle has a point of tangency at (5,1). The slope of this tangent line is The slope of a line with a y-intercept at (0, -2) is. nother point on the line is. (10, 2). (2,3). (4,8). (-2, -7) 5. The area of a circle with the equation (x + 3) 2 + (y 4) 2 = 10 is....

2 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam 6. If the right triangle in the figure at the right is rotated 180 o about the origin, which of the following will be the rotated figure? Problem #6 7. The diagonals of a quadrilateral are perpendicular bisectors of each other. The quadrilateral is best described as a. square. rectangle. kite. rhombus 8. Each interior angle of a regular polygon measures 156 o. The number of sides of the polygon is particular median of a triangle divides the triangle into two congruent triangles. The triangle is best described as an. equilateral triangle. isosceles triangle. obtuse triangle. acute triangle 10. The centroid of a triangle is. the point of intersection of the angle bisectors of the triangle. the point of intersection of the perpendicular bisectors of the sides of the triangle. the center of the circle that is tangent to the 3 sides of the triangle. the center of the circle passing through the 3 vertices of the triangle 11. is a trapezoid with the indicated lengths. The length of E is 180 E F H G Problem #11 2

3 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam 12. In the figure a median is drawn from. How long is this median?.... Not enough information (2,7) (-1,-4) Problem #12 (20,1) 13. In the figure the ray makes a 60 o angle with the positive x-axis. The point of intersection of the ray and the circle is... O (2,0). Problem # In the figure at the right the vertical and horizontal distances between the dots is one-unit. Which of the following measurements is irrational?... rea( ). Perimeter( ) E. ll are rational Problem # The altitude of an equilateral triangle is 12. To the nearest hundredth, the perimeter of a square that has the same area as the equilateral triangle is is an isosceles triangle with vertex angle. If the measure of the exterior angle is 148 o. What is the measure of the angle?. 74 o. 116 o. 32 o. 106 o 17. prism has 30 edges. The number of sides of the polygonal base is

4 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam 18. clock has a circular face and a minute hand that is 10 inches in length. To the nearest hundredth, what is the area swept out by the minute hand in 8 minutes? sq. in sq. in sq. in sq. in 19. is an isosceles trapezoid with the measurements shown. The angles of the trapezoid have the measures of. 60 o, 60 o, 120 o, 120 o. 30 o, 30 o, 150 o, 150 o. 45 o, 45 o, 135 o, 135 o. 72 o, 72 o, 108 o, 108 o 10 5 Problem # Which of the following geometric figures has exactly 2 lines of symmetry?. equilateral triangle. square. isosceles triangle. isosceles trapezoid 21. onsider the triangles as shown at the right. Which of the following statements is true? Problem #21. F = 35. FE = 12. ngle has a measure greater than ngle E. rea( = 4rea( ) F 57 E circle with a diameter of 30 has a central angle that intercepts an arc that has a length of. The measure of the central angle is. 36 o. 72 o. 108 o. 144 o 23. The radius of the circle is 10 and the inscribed angle () measures 54 o. The area of the shaded region is Problem #23 4

5 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam 24. The figure consists of two semicircles with their diameters on. If = 20 and O is the midpoint of, what is the area of the shaded region, to the nearest hundredth? O Problem # What is the angle of elevation, to the nearest minute, of a person at, to see an object at?. 38 o o o o 42 Problem #25 5

6 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam Tie-reaker Questions Name School In each of the following you must show supporting work for your answers to receive credit. The questions will be used in the order given to resolve ties for 1 st, 2 nd, and/or 3 rd place. e sure that your name is printed on each of the tiebreaker pages. 1. right triangle is created from a piece of wire that is 24 inches in length. If one leg is twice the shorter leg, what is the area of the triangle, to the nearest thousandth of a square inch? Tie reaker #1 6

7 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam Tie-reaker Questions Name School 2. is a rectangle. P = PE = GR = R = E = G = and H = HS = S = Q = QF = F =. a. Explain why EFGH is a parallelogram. P E H Q S G Tie reaker #2 R F b. Find EG. 7

8 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam Tie-reaker Questions Name School 3. onsider the following sequence of pictures. a. How many small triangles [ ] are in the bottom row of the 35 th picture? Explain Tie reaker #3 4 b. How many small triangles [ ] are in the 35 th picture? Explain! 8

9 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam KEY Multiple hoice E E

10 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam KEY Tie reakers 1. right triangle is created from a piece of wire that is 24 inches in length. If one leg is twice the shorter leg, what is the area of the triangle, to the nearest thousandth of a square inch? y x 2x Tie reaker #1 = is a rectangle. P = PE = GR = R = E = G = and H = HS = S = Q = QF = F =. a. Explain why EFGH is a parallelogram. P E Use a slope argument or find HE, GF and EF, H H Q S F Slope (EH) = Slope(FG) = G Tie reaker #2 R Slope (HG) = Slope(EF) = Therefore, and So, HEFG is a parallelogram because the opposite pairs of sides are parallel. istance argument: ; HE = FG ; ; HG = EF. So, HEFG is a parallelogram because opposite pairs of sides are equal in length. b. Find EG. Note: EG = R. 10

11 rkansas ouncil of Teachers of Mathematics 2013 State ontest - Geometry Exam 3. onsider the following sequence of pictures. a. How many small triangles [ ] are in the bottom row of the 35 th picture? Explain! Tie reaker #3 4 1 st row 1 = 2(1) nd row 3 = 2(2) rd row 5 = 2(3) th row 7 = 2(4) - 1 ontinuing the pattern, 35 th row 2(35) 1 = 69. b. How many small triangles [ ] are in the 35 th picture? Explain! 1 st row 1 = st and 2 nd row - 4 = st, 2 nd, and 3 rd row 9 = st, 2 nd, 3 rd,and 4 th row 16 = 4 2 ontinuing the pattern the number of triangles in the 35 th picture is 35 2 =