Name: Partners: Math 2 Date: Review 5 Version A [A] Circle whether each statement is true or false. 1. A chord is part of a secant. 2. An inscribed triangle must have a right angle. 3. An inscribed polygon has all its vertices on the circle. 4. The vertex of a central angle is the center of the circle. 5. Opposite angles in an inscribed polygon are complementary. 6. Every point outside a circle lies on two lines tangent to the circle. 7. A tangent always forms a right angle with the radius it intersects. [B] Sketch one of each of the following in one color, and another in a second color. 1. central angle 2. secant 3. arc 4. inscribed polygon
[C] Show all work, using appropriate notation and equations only, to show that the given answers are correct. Assume C and G are centers and E, F, R, and U are points of tangency. 1. a) CF = 42 b) AE = 56 E D C B 42 A 28 F 2. a) m KI = 68 b) m KGH = 34 J 34 G H I K 3. a) m OMN = 50 b) m OML = 130 L M O 47 N 53 P 4. a) m SUV = 132 b) m UWV = 64 Q 66 R 75 S 48 T U V W [D] Do the following to organize your group s reviews. 1. Make sure your name and your partners names are at the top of your review the first day. 2. Staple the reviews in order, all facing the same way. Put the staple in the very top left corner if everyone is finished or if the review is due; otherwise put the staple in the top right corner. 61
Name: Math 2 Date: Review 5 Version B [A] Circle whether each statement is true or false. 1. A chord is part of a secant. 2. An inscribed triangle must have a right angle. 3. An inscribed polygon has all its vertices on the circle. 4. The vertex of a central angle is the center of the circle. 5. Opposite angles in an inscribed polygon are complementary. 6. Every point outside a circle lies on two lines tangent to the circle. 7. A tangent always forms a right angle with the radius it intersects. [B] Sketch one of each of the following in one color, and another in a second color. 1. inscribed angle 2. tangent line segment 3. minor arc 4. inscribed triangle
[C] Show all work, using appropriate notation and equations only, to show that the given answers are correct. Assume C and G are centers and E, F, R, and U are points of tangency. 1. a) AE = 4 b) AB = 2 E D C B 3 A 4 F 2. a) m KGH = 70 b) m HJI = 35 J G H I K 70 3. a) m OML = 144 b) mon = 28 L 36 M O N 44 P 4. a) m SUV = 130 b) mvu = 70 Q 64 R 76 S 50 T U V W [D] Bonus. A central angle has a measure of 1 RADIAN if it intercepts an arc with length equal to the length of the radius. Show your calculations or explain your reasoning for the following. 1. How many degrees is one radian? 2. Evaluate sin 1.5. 61
Name: Math 2 Date: Review 5 Version C [A] Circle whether each statement is true or false. 1. A chord is part of a secant. 2. An inscribed triangle must have a right angle. 3. An inscribed polygon has all its vertices on the circle. 4. The vertex of a central angle is the center of the circle. 5. Opposite angles in an inscribed polygon are complementary. 6. Every point outside a circle lies on two lines tangent to the circle. 7. A tangent always forms a right angle with the radius it intersects. [B] Sketch one of each of the following in one color, and another in a second color. 1. circumscribed angle 2. tangent ray 3. semicircle 4. inscribed rectangle
[C] Show all work, using appropriate notation and equations only, to show that the given answers are correct. Assume C and G are centers and E, F, R, and U are points of tangency. 1. a) AF = 16 b) AB = 8 E D 16 B C 12 A F 2. a) m KGH = 72 b) m HJI = 36 J G H I K 72 3. a) m NMP = 78 b) mlp = 121 L O 102 M 83 N P 4. a) m SUV = 131 b) mvu = 66 Q 65 R 75 S 49 T U V W [D] Bonus. A central angle has a measure of 1 RADIAN if it intercepts an arc with length equal to the length of the radius. Show your calculations or explain your reasoning for the following. 1. How many degrees is one radian? 2. Evaluate cos 0.25. 62
Name: Math 2 Date: Review 5 Version D [A] Circle whether each statement is true or false. 1. A chord is part of a secant. 2. An inscribed triangle must have a right angle. 3. An inscribed polygon has all its vertices on the circle. 4. The vertex of a central angle is the center of the circle. 5. Opposite angles in an inscribed polygon are complementary. 6. Every point outside a circle lies on two lines tangent to the circle. 7. A tangent always forms a right angle with the radius it intersects. [B] Sketch one of each of the following in one color, and another in a second color. 1. inscribed right angle 2. tangent line 3. major arc 4. inscribed pentagon
[C] Show all work, using appropriate notation and equations only, to show that the given answers are correct. Assume C and G are centers and E, F, R, and U are points of tangency. 1. a) CF = 10.5 b) CA = 17.5 E D 7 B C A 14 F 2. a) m KI = 71 b) m HJI = 35.5 J 71 G H I K 3. a) m OMN = 119 b) mlo = 42 N O M 80 L 119 P 4. a) m SUV = 133 b) mrt = 72 Q 63 R S 47 T U V W [D] Bonus. A central angle has a measure of 1 RADIAN if it intercepts an arc with length equal to the length of the radius. Show your calculations or explain your reasoning for the following. 1. How many degrees is one radian? 2. Evaluate tan 4.5. 65 62