PARALLEL LINES & ANGLES

Transcription

1 PARALLEL LINES & ANGLES 1. In the figure above, PS and TR intersect at O and ON is perpendicular to PS. What is the value of y x? (A) 0 (B) 70 (C) 90 (D) 100 (E) In the figure above, if l // m, then the sum of the measures of angles and 4 must equal the sum of the measures of which of the following pairs of angles? (A) 5 and 6 (B) 5 and 7 (C) 6 and 7 (D) 6 and 8 (E) 7 and In the figure above, l n and x > 90. Which of the following must be true? (A) y < 90 (B) y > 90 (C) y = 90 (D) n m (E) l//m 109 In the figure above, three line segments meet at a point to form three angles. What is the value of x? (A) 0 (B) 36 (C) 40 (D) 45 (E) 60 11

2 009- PARALLEL LINES & ANGLES 5. What is the value of x in the figure above? Note: Figure not drawn to scale. 8. In the figure above, m // n and l bisects <ABC. If 45 < y < 55, what is one possible value for x? 6. In the figure above, l //m and r = 50. What is the value of s + t + u? (A) 30 (B) 40 (C) 50 (D) 70 (E) Three lines intersect in a point as shown in the figure above. Which of the following pairs of angle measures is NOT sufficient for determining all six angle measures? (A) t and z (B) t and y (C) s and x (D) r and t (E) r and s 9. In the figure above, if z = 30, what is the value of x + y? (A) 60 (B) 150 (C) 180 (D) 10 (E)

3 009- PARALLEL LINES & ANGLES 10. In the figure above, if AB is a line, what is the value of y? (A) 108 (B) 114 (C) 117 (D) 10 (E) In the figure above, y + z =? (A) 180 (B) 195 (C) 15 (D) 30 (E) In the figure above, l // m. If x = 80 and y = 70, what is the value of z? (A) 30 (B) 60 (C) 75 (D) 90 (E) In the figure above, if x = 70 and y = 40 and the dotted lines bisect the angles with measures x and y, what is the value of z? (A) 30 (B) 40 (C) 45 (D) 50 (E)

4 009- PARALLEL LINES & ANGLES 14. In the figure above,ad,be, and CF intersect at point O. If the measure of <AOB is 80 and CF bisects <BOD, what is the measure of <EOF? (A) 40 (B) 50 (C) 60 (D) 70 (E) In the figure above l // m. If v = w, which of the following must be equal to q? (A) v + t (B) v - t (C) t (D) v (E) s + t. 15. In the figure above, if l // m, what does z equal in terms of x and y? (A) x + y (B) x y (C) 180 x (D) 180 x + y (E) 180 x y 17. In the figure above, AE and BG intersect at C. If x = 80 and CF bisects ECG, what is the value of y? 11 4

5 009- PARALLEL LINES & ANGLES 18. In the figure above, l // m. If p (not shown) is another line in the plane, what is the least number of points at which p can intersect these four lines? (A) None (B) One (C) Two (D) Three (E) Four 0. In the figure above, the measure of SQR is 5 the measure of measure of PQR. If the PQR is 3 the measure of a right angle, what is the measure of (A) 4 (B) 36 (C) 48 (D) 60 (E) 96. SQR? 19. In the figure above, OA OC and OB OD. If x = 35, what is the value of z? (A) 55 (B) 45 (C) 35 (D) 30 (E) In the figure above, lines k, l, and m are parallel. If y = 15, what is the value of x + z? (A) 90 (B) 95 (C) 100 (D) 105 (E) 110 5

6 009- PARALLEL LINES & ANGLES. In the figure above, lines l and m intersect. If y = 44, what is the value of x? (A) 17 (B) 18 (C) 130 (D) 13 (E) In the figure above, what is the value of y? (A) 40 (B) 45 (C) 50 (D) 60 (E) The figure above shows five lines. If l // m, which of the following is NOT equal to 90? (A) r (B) s (C) t (D) u (E) v 5. In the figure above, if l // m and r = 91, then t + u = (A) 178 (B) 179 (C) 180 (D) 181 (E)

7 TRIANGLES 1. In the equilateral triangle RST above, what is the value of y? (A) 60 (B) 70 (C) 75 (D) 80 (E) 85 Note: Figure not drown to scale. 3. In the xy-plane above, the area of OST is 8. What is the value of a?. In the figure above, N lies onmo. In terms of x, which of the following must be equivalent to y? (A) x (B) x 5 (C) 3x 5 (D) 90 x (E) x 4. In the figure above, what is the value of x + y? (A) 90 (B) 100 (C) 110 (D) 10 (E)

8 009- TRIANGLES Note: Figure not drown to scale. 5. In the figure above, x 90 and y z 1. If z is an integer, what is the greatest possible value of y? (A) 30 (B) 45 (C) 60 (D) 61 (E) In triangle ABC above, if AD = 6, DC = 3, and BC = 4, what is the area of triangle ABD? (A) 36 (B) 18 (C) 1 (D) 6 (E) 3 6. If the length of AB is 5 and the length of BC is 6, which of the following could be the length of AC? (A) 10 (B) 1 (C) 13 (D) 15 (E) In ABC above, what is the length of AD? 116

9 009- TRIANGLES 9. In ABC above, AB = 3, and D is the midpoint of AC. What is the length of BC? (A) 3 3 (approximately 5.0) (B) 4 (approximately 5.66) (C) 4 3 (approximately 6.93) (D) 6 (approximately 8.49) (E) 5 3 (approximately 8.66) 11.In the triangle above, x = (A) 59 (B) 60 (C) 61 (D) 6 (E) In isosceles triangle ABC, the measure of angle A is 80. If another angle of the triangle measures x, where x 80, what is one possible value of x? In the figure above,the coordinates of P are ( 10 a,0) and the coordinates of Q are ( 10, a ).A point in square ORST is to be chosen at random. If the probability that the point will be in the shaded triangle is 5 1, what is the value of a? (A) 5 (B) 10 (C) 5 (D) 10 (E) 5 3

10 009- TRIANGLES 15.If the length oflm is 7 and the length of MN is 8, which of the following could be the length of LN? 13.In the figure above, if the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD? (A) 3 (B) (C) 17 (D) 16 (E) 14 7 (A) (B) 5 (C) 7 15 (D) (E) A circle (not drawn) passes through point A in the figure above. What could be the total number of points of intersection of this circle and ΔABC? 14.In the figure above, sideac of ABC is on line l. What is x in terms of k? (A) 60 k (B)k (C) 60 k (D) 10 k (E) 10 k I. 1 II. 3 III. 4 (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III 118 4

11 009- TRIANGLES 17.In triangle XYZ above, XW =, WZ = 8, and XY = 6. What is the area of triangle WYZ? (A) 6 (B) 1 (C) 18 (D) 4 (E) In the figure above, ABDE is a square, ΔBCD is a right triangle, and AB = BC. If a point is chosen at random from polygon ACDE, what is the probability that the chosen point is in the shaded region? (A) 1 (B) 3 1 (C) 4 1 (D) 5 1 (E) In the figure above, ΔABC is similar to ΔDEF. What is the length of side EF? 119 5

12 009- TRIANGLES 0.The figure above is a right triangle. What is the value of 5 x? (A) 3 (B) 34 (C) 39 (D) 50 (E) 64 1.In the figure above, a < 40 and b = c + 1. If c is an integer, what is the least possible value of b? (A) 30 (B) 39 (C) 50 (D) 61 (E)

13 TRIANGLES 3. A triangle has a perimeter of 13 and one side of length 3. If the lengths of the other two sides are equal, what is the length of each of them? 1. Which of the following inequalities is true about the lengths a and b of the sides of the triangle above? (A) 0 ( a b) 0 (B) 0 ( a b) 40 (C) 40 ( a b) 100 (D) 100 ( a b) 400 (E) 400 ( a b ) (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 4. The three angles of a triangle have measures of x, x, and y, where x > 55. If x and y are integers, what is one possible value of y?. Triangles ABC and ACD in the figure above are equilateral. What is the ratio of BD to AC? (A) to 1 (B) 3 to 1 (C) to (D) 3 to (E) 3 to 5. In ΔABC above, AC=5, PC=3, and BP = 4 3.What is the length of AB? 11 11

14 009- TRIANGLES 6. In the figure above, triangles ABC and CDE are equilateral and line segment AE has length 5. What is the sum of the perimeters of the two triangles? 8. In PQR above, PR = QR. Which of the following must be true? (A) u = x (B) x = v (C) x = z (D) y = x (E) y = z 7. In the figure above, which of the following is greatest? (A) a (B) b (C) c (D) d (E) e 9. In the figure above, AC 6 andbc 3. Point P (not shown) lies on AB between A and B such thatcp AB. Which of the following could be the length of CP? (A) (B) 4 (C) 5 (D) 7 (E) 8 1

15 009- TRIANGLES 10.What is the greatest possible area of a triangle with one side of length 7 and another side of length 10? (A) 17 (B) 34 (C) 35 (D) 70 (E) In ABC above, AB AC, E is the midpoint of AB, and D is the midpoint of AC. If AE x anded 4, what is length BC? (A) 6 (B) 8 (C) x (D) 4x (E) 4x 11.In the figure above,ab,cd, and EF intersect at P. If r= 90, s=50, t= 60, u= 45, and w= 50, what is the value of x? (A) 45 (B) 50 (C) 65 (D) 75 (E) It cannot be determined from the information given If x = 0 and y = 30 in the figure above, what is the value of z? (A) 60 (B) 70 (C) 80 (D) 90 3

16 009- TRIANGLES (E) In the right triangle above, if x = 3, what is the value of y? (A) 13 (approximately 3.61) (B) 15 (approximately 3.87) (C) 4 (D) 17 (approximately 4.1) (E) 5 In the figure above, PQR is equilateral and SR and TV intersect at point P. What is the value of y? Each angle of ABC above has the same measure as angle in XYZ (not shown). If the length of one side of XYZ is 4, what is one possible perimeter of XYZ? In the figure above, AD = 1 and DC = 3. What is the value of z? (A) 15 (B) 0 (C) 5 (D) 30 (E)

17 009- TRIANGLES 18. In the figure above, what is the value of c in terms of a and b? (A) a + 3b 180 (B) a + b 180 (C) 180 a b (D) 360 a b (E) 360 a 3b 0.The lengths of the sides of a right triangle are consecutive even integers, and the length of the shortest side is x. Which of the following equations could be used to find x? (A) x + x + 1 = x + (B) x + (x + 1) = (x + ) (C) x + (x + ) = (x + 4) (D) x + x + = x + 4 (E) x = (x + )(x + 4) If y = 60 in DEF above, how much greater is the perimeter of ABC than the perimeter of DEF? QS 1 PT In PQR above, and QV 3 PR What is the value of the fraction area PST? area PQR 3 4. (A) 0 (B) 3 (C) 6 (D) 8 (E)

18 TRIANGLES In the figure above, KN JL and LM JL. If the lengths of LN and LM are equal, what is the value of x? In the figure above, AB = BC and DE = EF = DF. If the measure of <ABC is 30 and the measure of <BDE is 50, what is the measure of <DFA? (A) 30 (B) 35 (C) 40 (D) 45 (E) In the figure above, what is the value of t + u? (A) 80 (B) 90 (C) 100 (D) 110 (E) 10 In the figure above, what is the sum, in terms of n, of the degree measures of the four angles marked with arrows? (A) n (B) n (C) 180 n (D) 360 n (E) 360 n 16 11

19 009- TRIANGLES In XYZ above, XZ is 7 6 of h, the length of the altitude. What is the area of XYZ in terms of h? h (A) 3 3h (B) 7 3h (C) 7 In the figure above, what is the value of z? (A) 55 (B) 60 (C) 65 (D) 70 (E) 75 6h (D) 7 1h (E) P(3, ) Q(7, ) R(7, 4) The coordinates of points P, Q, and R in the xy plane are given above. What is the perimeter of PQR? (A) 1 (B) 14 (C) (approximately 10.47) (D) (approximately 11.66) (E) 164 (approximately 1.81) If AB = BC and BD bisects AC in the figure above, which of the following CANNOT be concluded? (A) w = x (B) w = z (C) x = y (D) AD = DC (E) BD AC 17

20 009- TRIANGLES In the figure above, if z = 30, what is the value of x + y? (A) 60 (B) 150 (C) 180 (D) 10 (E) 330 For the triangles above, the perimeter of ABC equals the perimeter of DEF. If ABC is equilateral, what is the length ofab? (A) 4 (B) 5 (C) 7 (D) 9 (E) In the figure above, AE and CDare each perpendicular to CE. If x = y, the length of AB is 4, and the length of BD is 8, what is the length ofce? (A) 3 (approximately 4.4) (B) 6 (approximately 8.49) (C) 8 (approximately 11.31) (D) 10 (approximately 14.14) (E) 1 (approximately 16.97) In the triangles above, what is the average (arithmetic mean) of u, v, w, x, and y? (A) 1 (B) 45 (C) 50 (D) 5 (E)

21 009- TRIANGLES In the figure above, points P, A, and B are equally spaced on line l and points P, Q, and R are equally spaced on line m. If PB = 4,PR = 6, and AQ = 4, what is the perimeter of quadrilateral QABR? (A) 13 (B) 14 (C) 15 (D) 16 (E) 17 In the figure above, y + z =? (A) 180 (B) 195 (C) 15 (D) 30 (E) In the figure above, the perimeter of the triangle is 4 +. What is the value of x? (A) (B) 4 (C) (D) (E) + 16.A square and an equilateral triangle have equal perimeters. If the square has sides of length 3, what is the length of one side of the triangle? (A) (B) 3 (C) 4 (D) 5 (E)

22 009- TRIANGLES 17.The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF. If the perimeter of DEF is 10, what is the length of one side of ABC? 0. 1 (A) 3 3 (B) 10 (C) 15 (D) 30 (E) In ABC above, what is the value of x? (A) 5 (B) 30 (C) 35 (D) 40 (E) 60 In the figure above, if the legs of triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC? (A), 5, and 9 (B), 5,and 7 (C) 3, 3, and 3 (D) 3, 4,and 5 (E) 4, 5,and The figure above is a right triangle. What is the value of 49 + x? (A) 50 (B) 51 (C) 7 (D) 98 (E) If the degree measures of the angles of a triangle are in the ratio :3:4, by how many degrees does the measure of the largest angle exceed the measure of the smallest angle? (A) 0 (B) 30 (C) 40 (D) 50 (E)

23 POLYGONS 1. In the figure above, a small square is inside a larger square. What is the area, in terms of x, of the shaded region? (A) x 10 (B) 10 x (C) 5 x (D) x 5 (E) 5 x 3. In the figure above, the circle is tangent to sides BC and AD of the 8-by-1 rectangle, ABCD. What is the area of the circle? (A) 16 (B) 0 (C) 36 (D) 64 (E) 96. In the figure above, rectangle ABCD is made up of seven non-overlapping rectangles. The two smallest rectangles have the same area. Each of the other rectangles has twice the area of the next smaller rectangle. The area of the shaded rectangle is what fraction of the area of rectangle ABCD? 1 (A) 18 1 (B) 64 1 (C) 3 4. What is the perimeter of the figure above? (A) 4 (B) 5 (C) 8 (D) 30 (E) 36 1 (D) 16 1 (E)

24 009- POLYGONS 5. In the figure above, ABCD is a rectangle with BC = 4 and AB = 6. Points P, Q, and R are different points on a line (not shown) that is parallel toad. Points P and Q are symmetric about line AB and points Q and R are symmetric about line CD. What is the length of PR?. (A) 6 (B) 8 (C) 10 (D) 1 (E) 0 7. In rectangle PQRS above, arcs QT and RT are quarter circles with centers at P and S, respectively. If the radius of each quarter circle is 1, what is the area of the shaded region? (A) 1 4 (B) (C) 4 (D) 4 (E) 3 6. The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 1L units long and 19L units wide. How many rectangles of dimension L by W are needed? (A) 30 (B) 36 (C) 100 (D) 150 (E) If the areas of two regions are equal and the sum of the areas of the regions is 5, what is the average (arithmetic mean) of the areas of the two regions? (A) 0 (B) 5 (C) 4 5 (D) 5 (E) 10 13

25 009- POLYGONS 9. The smallest squares in Figure A and Figure B are all equal in size. If the area of Figure A is 6 square centimeters, what is the area of Figure B? (A) 1 sq cm (B) 14 sq cm (C) 16 sq cm (D) 18 sq cm (E) 0 sq cm 11. In the figure above, ABCDEF is a regular hexagon, and its center is point O. What is the value of x? (A) 80 (B) 60 (C) 40 (D) 30 (E) In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded region is (A) (B) (C) (D) (E) If the five line segments in the figure above are all congruent, what is the ratio of the length of AC (not shown) to the length of BD? (A) to 1 (B) 3 to1 (C) to (D) 3 to (E) 3 to 3

26 009- POLYGONS 15. In rectangle ABCD, point E is the midpoint of BC. If the area of quadrilateral 13. The figures above represent three pieces of cardboard. All angles of the cardboard pieces are right angles, all short sides have length 1, and all long sides have length. Which of the following figures could be made from only the three pieces of cardboard without over lapping or cutting them? ABED is, what is the area of rectangle 3 ABCD? 1 (A) 3 (B) 4 8 (C) 9 (D) 1 (E) 3 8 (A) None (B) I only (C) II only (D) III only (E) I and II = 14. If there is no waste, how many square yards of carpeting is needed to cover a rectangular floor that is 1 feet by 18 feet? (1 yard = 3 feet) (A) 8 (B) 16 (C) 4 (D) 30 (E) In the figure above, EF divides square ABCD into two rectangles, and CD bisects EF. If AB is 4, what is the area of DCF? (A) 9 (B) 8 (C) 7 (D) 6 (E)

27 009- POLYGONS 17. If the perimeter of the rectangle above is 7, what is the value of x? (A) 9 (B) 15ππ (C) 18 (D) 1 (E) In the figure above, the length of CD is 4, and the length of each side of quadrilateral ABCE is 5. What is the area of quadrilateral ABCD? (A) 3 (B) 8 (C) 7 (D) 6 (E) 18. In the figure above, a square with sides of length 6 units is divided into 9 squares. What is the area of the circle (not shown) that passes through the points A, B, C, and D, which are the centers of the four corner squares? (A) 6π square units (B) 8π square units (C) 9π square units (D) 10π square units (E) 18π square units 0. If all four interior angles of quadrilateral P have the same measure, which of the following statements must be true? I. All sides of P have equal length. II. The diagonals of P are perpendicular. III. The measure of each interior angle of P is. (A) None (B) I only (C) II only (D) III only (E) I, II, and III 135 5

28 POLYGONS 1. In the figure above, a small square is inside a larger square. What is the area, in terms of x, of the shaded region? (A) x 10 (B) 10 x (C) 5 x (D) x 5 (E) 5 x 3. In the figure above, the circle is tangent to sides BC and AD of the 8-by-1 rectangle, ABCD. What is the area of the circle? (A) 16 (B) 0 (C) 36 (D) 64 (E) 96. In the figure above, rectangle ABCD is made up of seven non-overlapping rectangles. The two smallest rectangles have the same area. Each of the other rectangles has twice the area of the next smaller rectangle. The area of the shaded rectangle is what fraction of the area of rectangle ABCD? 1 (A) 18 1 (B) 64 1 (C) 3 4. What is the perimeter of the figure above? (A) 4 (B) 5 (C) 8 (D) 30 (E) 36 1 (D) 16 1 (E)

29 009- POLYGONS 5. In the figure above, ABCD is a rectangle with BC = 4 and AB = 6. Points P, Q, and R are different points on a line (not shown) that is parallel toad. Points P and Q are symmetric about line AB and points Q and R are symmetric about line CD. What is the length of PR?. (A) 6 (B) 8 (C) 10 (D) 1 (E) 0 7. In rectangle PQRS above, arcs QT and RT are quarter circles with centers at P and S, respectively. If the radius of each quarter circle is 1, what is the area of the shaded region? (A) 1 4 (B) (C) 4 (D) 4 (E) 3 6. The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 1L units long and 19L units wide. How many rectangles of dimension L by W are needed? (A) 30 (B) 36 (C) 100 (D) 150 (E) If the areas of two regions are equal and the sum of the areas of the regions is 5, what is the average (arithmetic mean) of the areas of the two regions? (A) 0 (B) 5 (C) 4 5 (D) 5 (E)

30 009- POLYGONS 9. The smallest squares in Figure A and Figure B are all equal in size. If the area of Figure A is 6 square centimeters, what is the area of Figure B? (A) 1 sq cm (B) 14 sq cm (C) 16 sq cm (D) 18 sq cm (E) 0 sq cm 11. In the figure above, ABCDEF is a regular hexagon, and its center is point O. What is the value of x? (A) 80 (B) 60 (C) 40 (D) 30 (E) In the figure above, arc SBT is one quarter of a circle with center R and radius 6. If the length plus the width of rectangle ABCR is 8, then the perimeter of the shaded region is (A) (B) (C) (D) (E) If the five line segments in the figure above are all congruent, what is the ratio of the length of AC (not shown) to the length of BD? (A) to 1 (B) 3 to1 (C) to (D) 3 to (E) 3 to 3

31 009- POLYGONS 15. In rectangle ABCD, point E is the midpoint of BC. If the area of quadrilateral 13. The figures above represent three pieces of cardboard. All angles of the cardboard pieces are right angles, all short sides have length 1, and all long sides have length. Which of the following figures could be made from only the three pieces of cardboard without over lapping or cutting them? ABED is, what is the area of rectangle 3 ABCD? 1 (A) 3 (B) 4 8 (C) 9 (D) 1 (E) 3 8 (A) None (B) I only (C) II only (D) III only (E) I and II = 14. If there is no waste, how many square yards of carpeting is needed to cover a rectangular floor that is 1 feet by 18 feet? (1 yard = 3 feet) (A) 8 (B) 16 (C) 4 (D) 30 (E) In the figure above, EF divides square ABCD into two rectangles, and CD bisects EF. If AB is 4, what is the area of DCF? (A) 9 (B) 8 (C) 7 (D) 6 (E)

32 009- POLYGONS 17. If the perimeter of the rectangle above is 7, what is the value of x? (A) 9 (B) 15ππ (C) 18 (D) 1 (E) In the figure above, the length of CD is 4, and the length of each side of quadrilateral ABCE is 5. What is the area of quadrilateral ABCD? (A) 3 (B) 8 (C) 7 (D) 6 (E) 18. In the figure above, a square with sides of length 6 units is divided into 9 squares. What is the area of the circle (not shown) that passes through the points A, B, C, and D, which are the centers of the four corner squares? (A) 6π square units (B) 8π square units (C) 9π square units (D) 10π square units (E) 18π square units 0. If all four interior angles of quadrilateral P have the same measure, which of the following statements must be true? I. All sides of P have equal length. II. The diagonals of P are perpendicular. III. The measure of each interior angle of P is. (A) None (B) I only (C) II only (D) III only (E) I, II, and III 140 5

33 POLYGONS Questions 1- refer to the following figures and information. 3. In the figure above, if the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD? The figure on the left is called an ell. The lengths of some of its sides are given, and all the angles are right angles. For any positive integer n, an n-ell is the figure formed by positioning n ells adjacent to each other as shown in the 3-ell on the right. (A) (B) 5 (C) 7 (D) (E) What is the perimeter of the 3-ell? (A) 18 (B) 1 (C) 4 (D) 7 (E) 30. The perimeter of an 80-ell is 36 and the perimeter of a 0-ell is 86. What is the perimeter of a 100-ell? (A) 406 (B) 409 (C) 41 (D) 416 (E) The smallest squares in Figure A and Figure B are all equal in size. If the area of Figure A is 33 square centimeters, what is the area, in square centimeters, of Figure B? (A) 15 (B) 18 (C) 1 (D) 4 (E)

34 009- POLYGONS 5. In the figure above, ABDE is a square, BCD is a right triangle, and AB=BC. If a point is chosen at random from polygon ACDE, what is the probability that the chosen point is in the shaded region? (A) (B) (C) (D) (E) 7. In the figure above, regular pentagon ABCDE is divided into three nonoverlapping triangles. Which of the following is true about the three triangles? (A) They have equal areas. (B) They have equal perimeters. (C) They are similar. (D) They are isosceles. (E) They each have at least one angle of measure The length of a rectangular garden is 3 feet more than its width. If the length of the garden is 9 feet, what is the area of the garden in square feet? (A) 7 (B) 36 (C) 54 (D) 81 (E) Triangles ABC and ACD in the figure above are equilateral. What is the ratio of BD to AC? (A) to 1 (B) to 1 (C) to (D) to (E) to 14

35 009- POLYGONS 9. The length of a rectangular rug is feet more than its width. If the length of the rug is 8 feet, what is the area of the rug in square feet? (A) 16 (B) 48 (C) 66 (D) 80 (E) What is the perimeter of the trapezoid above? (A) 5 (B) 7 (C) 75 (D) 80 (E) In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE? 10. In rectangle ABCD above, the area of the shaded region is given by. If the area of the shaded region is 7π, what is the total area, to the nearest number, of the unshaded regions of rectangle ABCD? (A) 4 (B) 6 (C) 8 (D) 9 (E) 10 (A) 4 (B) 5 (C) 6 (D) 7 (E) The perimeter of a rectangular plot of land is 50 meters. If the length of one side of the plot is 40 meters, what is the area of the plot, in square meters? 143 3

36 009- POLYGONS 14. In the figure above, the lengths and widths of rectangles A, B, C, and D are whole numbers. The areas of rectangles A, B, and C are 35, 45, and 36, respectively. What is the area of the entire figure? 17. In the figure above, EBCD is a square and AE = 8. What is the area of EBCD? 15. In the figure above, what is the area of the shaded square? 18. In the figure above, PQRS is a rectangle. The area of RST is 7 and PT PS. What is the area of PQRS 16. In the figure above, PQST is a rectangle and URST is a square. PU = 5 and UT is a positive integer. If the area of PQST must be more than 10 but less than 30, what is one possible value of UT. 19. In the figure above, points A, D, and E lie on the same line. What is the value of x? 144 4