FGCU Invitational Geometry Individual 2014

Transcription

1 All numbers are assumed to be real. Diagrams are not drawn to scale. For all questions, NOTA represents none of the above answers is correct. For problems 1 and 2, refer to the figure in which AC BC and AB CD. C A B D 1) If AD = 10 cm and BD = cm, find CD. a) 0 cm b) 15 cm c) 0 cm d) 6 cm 2) If AB = 16 cm and BC = 6 cm, find BD. a) 9 cm b) 9 cm c) 8 cm d) 12 cm ) Name the polygon that satisfies the following set of properties It has four sides. Each diagonal divides the polygon into two congruent triangles. Diagonals bisect each other. Both pairs of opposite sides are parallel. a) square b) kite c) rhombus d) both a and c ) Find the missing coordinate so that the ordered pair (?, ) is a solution to y = 2x + 5. a) (, ) b) (0, ) c) ( 2, ) d) (2, ) 5) In the figure below, a = 7 and b =. Find tan A. A b c a) C a b) B c) 7 d) 7 Page 1 of 6

2 6) In PQR and STU, PQ = ST, PR = SU, and m P > m S. What is the relationship between QR and TU? a) QR = TU b) QR > TU c) QR < TU d) both b and c 7) A recreation room is in the shape of an isosceles triangle with the vertex angle measuring 90 and base 2 meters. Find the perimeter of the room. a) m b) 12 m c) m d) 6 m Use the figure in problems 8 and ) Find the measure of angle 1. a) 50 b) 60 c) 70 d) 110 9) Find the measure of angle. a) 50 b) 60 c) 70 d) ) How many planes pass through three distinct points not on the same line? a) 1 b) 2 c) d) none Page 2 of 6

3 11) Name the figure that satisfies the following set of properties It has four sides. All angles are right angles. Opposite angles are congruent. Diagonals are congruent. a) square b) kite c) rhombus d) both a and c 12) If you have two right triangles, ABC and LMN, and you know B = 90, M = 90, AB LM and BC. MN What theorem would you use to prove ABC LMN? a) Leg-Angle (LA) b) Leg-Leg (LL) c) Side-Side- Side (SSS) d) Angle-Side- Angle (ASA) 1) Find the complement of a) 97 8 b) 7 78 c) 97 2 d) 7 8 1) Classical Greek methods of construction do not have the ability to effectively perform which of the following operations? a) multiplication b) division c) square root d) cube root 15) Use the transitive law to complete the following: If 2 = w and w = x, then. a) w = 2 b) x = w c) 2 = x d) 2 = 2 16) What is the sum of the measures of the exterior angles of a nonagon? a) 60 b) 1620 c) 10 d) 1260 Page of 6

4 17) What is the measure of each interior angle of a regular nonagon? a) 60 b) 1260 c) 10 d) ) Find the general form of the equation of the line perpendicular to a line with a slope 7 and 6 passing through (5, 1). a) 6x 7y 7 = 0 d) 6x + 7y + 7 = 0 b) 6x 7y 1 = 0 c) 6x + 7y + 1 = 0 19) The base of an isosceles triangle is 20 cm and the perimeter is 70 cm. Find the length of each remaining side. a) 25 cm b) 0 cm c) 2 cm d) 20 cm 20) Solve the proportion: x+2 x = a) 11 b) 1 c) -11 d) 2 21) Suppose C and D are corresponding angles of congruent triangles with C opposite AB and D opposite. EF If AB = 16 and EF = 10 x, determine x. a) 26 b) 6 c) 16 d) -6 22) Find the geometric mean between 28 and 18. a) 1 b) 6 1 c) 6 7 d) 7 Page of 6

5 2) Give the contrapositive of the statement, If it is warm, then the car will start. a) If it is not warm, then the car will not start. b) It is not warm. c) If the car will not start, then it is not warm. d) If the car starts, then it is warm. 2) Name the polygon that satisfies the following set of properties It has four sides. Two pairs of adjacent sides are congruent. Diagonals are perpendicular bisectors of each other. Exactly one diagonal is an angle bisector. a) square b) kite c) rhombus d) both a and c 25) Find x in the figure below. x 20 5x + 0 a) x = 20 b) x = 10 c) x = 0 d) x = 15 Page 5 of 6

6 26) Refer to the figure below with X the midpoint of side, MN Y the midpoint of side, NO XY = 5x, and MO = 8x Find x. N X 5x Y M 8x + 16 O a) 112 b) 56 c) 12 d) 6 27) If A is an acute angle in a right triangle and cos A =, find sin A. a) 7 b) 7 c) d) For problems 28-0, assume that the two points P(1, 5) and Q( 2, ) are given. 28) What is the slope of the line passing through P and Q? a) 2 b) 2 c) 2 d) ) What is the distance between P and Q? a) b) 1 c) 65 d) 5 0) What are the coordinates of the midpoint of the line segment joining P and Q? a) ( 2, 1) b) (,1) c) (1,6) d) ( 1 2, ) Page 6 of 6