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Itg2 U3 Vocab Vocabulary WS Point Can be thought of as a dot that represents a location in a plane or in space Line * Is understood to be straight, to contain an infinite number of points, to extend infinitely in two directions and has no thickness. Line segment * A line with endpoints, thus its length is measurable. Ray * Consist of an initial point and all the points on a line to one side only. ( = ray BA) (ray AB) Itg2 U3 WS 1 (Practice 68) Write the name of each figure 1. Line TG = 2. Angles: L GHI and L IHG 3. Plane Can be thought of as a flat surface that extends infinitely in all directions. Collinear Points, segments, or rays that are on the same straight line are collinear. Intersect Where objects cross / meet. Planes -> Line Lines -> Point Endpoints The end of a line, ray, or segment. Points where you begin and end. Angle * Consist of two different rays that have the same initial point. (The initial point is the vertex of the angle). Two rays that have a common endpoint. Vertex The initial point where the two rays meet to make an angle. The point where two rays intersect. Ray QZ = Use the following picture to answer the questions 4-6 4. Name all the rays which have M as an endpoint. Rays MX, MV, MY, MW = 5. Name an angle formed by Angle: L VMY 6. Give two different names for L 1 Angles: L XMW and L WMX ------------------------------------------Give three different names for line l below. Lines: AB, BC and AC = 7. and . 8. Explain why the symbols and represent the same geometric figure. Segments are measurable and have a starting and ending point so these lengths are the same. 9. Explain why the symbols and do not represent the same geometric figure. Segment is measurable, whereas line goes on forever. Itg2 U3 WS 2 (Practice 69) Use a protractor to measure each angle 1. 115o 2. 7. 68o 8. 136o 9. Draw angle QMN, which has a measure of 140o 90o 10. Draw angle XYZ, which has a measure of 46o 3. 25 o 11. Use a protractor to measure L APY and L RPX . How do the compare? Use the following picture to answer the following question m L APY = 120 o and the m L RPX = 120 o. These two vertically opposite angles are congruent. 4. Find the measures (in degrees) of the following angles: (a) angle AFB 45 o (d) angle EFD 40 o (b) angle EFB 135 o (e) angle AFD 140 o (c) angle AFC 80 o Use a protractor to draw an angle of the measure. 5. 170 o 6. 80 o Itg2 U3 WS 3 (Practice 70) Tell whether two angles with the given measures are complementary, supplementary, or neither. 1. 80o, 10o complementary o o 2. 112 , 68 supplementary 3. 43o, 137o supplementary 4. 44o, 36o neither o o 5. 138 , 42 supplementary 6. 63o, 27o complementary 7. 114o, 96o neither o o 8. 18 , 72 complementary 9. 5o, 185o neither Find the measure of a complement of an angle of the given measure. 10. 53o 37o 11. 77o 13o o 12. 15 75o 13. 84o 6o o 14. 26 64o o 15. 62 28o 16. 33o 57o o 17. 19 71o L TOP 108o 19. L SOQ 108 o 20. L TOQ 72o 21. Find the measure of a complement of L Y. 32o 22. Find the measure of a supplement of L Y. 148o 43. If m L 1 = 38o and m L 2 = 52o, what can you conclude about L 1 and m L 2? The two angles are complementary. Acute 44. Obtuse Acute 45. Right Find the value of x in each situation below. Pictures are not drawn to scale, do not use a protractor. 46. x + 115 = 180 47. x + 72 = 180 x = 65 o x = 108 o 48. Find the measure of L ABD in the figure below. 26 o 32. 42. Straight Find the measure of a supplement of an angle of the given measure. 23. 27o 153o o 24. 94 86o 25. 114 o 66o o 26. 166 14o 27. 81 o 99o o 28. 135 45o o 29. 19 161o 30. 30 o 150o 31. Identify each angle below as acute, obtuse, right, or straight. 41. Give the measure of each angle. 18. Define each of the following. 32. Acute angle An angle with a measure less than 90 o. 33. Obtuse angle An angle with a measure greater than 90 o. 34. Right angle An angle with a measure equal to 90 o. 35. Straight angle An angle with a measure equal to 180 o. 36. Vertical angles Angles on opposite sides of an X. Their measures are equal 37. Complementary Two angles are complementary if the sum of their measures is 90 o. 38. Supplementary Two angles are supplementary if the sum of their measures is 180 o 39. Adjacent angles Two angles are adjacent if they share a common vertex and side. 40. Linear pair Two adjacent angles that are supplementary 50. 2x + 98 = 180 x = 41 5x – 8 = 32 x=8 49. x = 137 51. 4x – 25 = 35 x = 15 Itg2 U3 WS 4 (Practice 71) 1. Find the value of x and the measure of each angle. 2. 3. 4. 5. 4x + 1 = 65 L AEC and L DEC = 115 o x= 16 L AED and L CEB = 65 o LABC is complementary to LCBD. Sketch a picture, and write an equation to solve for x if m LABC = 4x and LCBD = 5x 4x + 5x = 90 o x = 10 LABC is supplementary to LCBD. Sketch a picture and write an equation to solve for x if L ABC = 4x and LCBD = 5x 4x + 5x = 180 o x = 20 LABC is a vertical angle to LDBE. Sketch a picture and write an equation to solve for x if LABC = 4x - 20 and LDBE = 2x + 40 4x + 5x = 90 o x = 10 Solve for x. * Move 33 to lower left corner (corresponding). Next set 33 = to 2x – 7 (vertical angle). 2x – 7 = 33; x = 20 6. Solve for x. 11x – 20 = 8x – 14; x = 2 7. Solve for x. * Move 10x – 20 to lower right corner (corresponding). Next: 10x – 20 + 2x + 20 = 180 (Linear Pair); x = 15 8. Solve for x. * Move 20x – 10 to lower corner (corresponding). Next: 20x – 10 + 10x + 10 = 180 (Linear Pair); x = 6 9. In the figure below, and L 4 = 110o. Find the measure of each angle. 10. In the figure below, , Find the measure of each angle. and L 2 = 120o. 11. Given that L 1 = 53o, L 3 = 140o and A || X. Find the measure of each angle. 12. Given: L1 || L2; L4 || L5; L3 L2 and L 3 = 40o, and L 1 = 20o , solve all other angles. Itg2 U3 WS 5 1. Describe the measure of each of the following angles. (a) Acute An angle measure < 90 degrees. (b) Right An angle measure = 90 degrees. (c) Obtuse An angle measure > 90 degrees. (d) Straight An angle measure = 180 degrees. 8. Solve for x. 9. Solve for x. 2. Given the figure below. 10. Solve for y. 11. (a) State two straight angles (b) State two acute angles (c) State two obtuse angles (d) State one right angle ABC, BED ADB, ADC ABD, CED ACD 3. Given the following choices for the figure below: (Vertical Opposites, Linear Pair, Supplementary, Complementary and Right angle), state all choices that apply to the following. (a) Angles 3 & 4 (b) Angles 1 & 3 (c) Angle 5 (d) Angles 1 & 4 (e) Angles 2 & 4 4. Solve for x. 5. Solve for x. 6. Solve for x. 7. Solve for x. Linear Pair & Supplementary Vertical Opposites Right angle Linear Pair & Supplementary Vertical Opposites Given the following information: Solve for the value of x, y and all angles? 4x + 31 = 6x – 11 (Vertical Opposites are ) - 4x + 11 - 4x + 11 42 = 2x 2 2 x = 21 = 4(x) + 31 or = 6(x) – 11 = 4(21) + 31 = 6(21) – 11 = 115 = 115 L ? + 115 = 180 (Linear Pair Ls are supplementary) - 115 - 115 L? = 65 If L ? = 65 and L ? = 6y + 29 then 6y + 29 = 65 – 29 – 29 6y = 36 6 6 y = 6 12. Given: L1 || L2; L3 || L5; L4 || L6; L1 L2 and L 4 = 120o, and L 15 = 30o , solve all other angles 13. Solve all angles below Itg2 U3 WS 6 1) In the picture below if BC is parallel to line EF, (a) What is the value of x? (b) What is the measure of angle ABC? (c) What is the measure of angle BED? (d) Label all the angle measurements. L ABC = L BEF (Corresponding angles are ) 3x – 12 = 2x + 12 - 2x + 12 - 2x + 12 x = 24 L ABC = L BEF = 3(x) – 12 or = 2(x) + 12 = 3(24) – 12 or = 2(24) + 12 = 60 = 60 L BED + L BEF = 180 (Linear Pairs are supplementary) L BED + 60 = 180 - 60 - 60 L BED = 120 2. Lines that look parallel are parallel, L 12 = 100o, L 14 = 30o. Solve all angles below 3. In the picture below if BD is parallel to line EG, (a) What is the value of x? (b) What is the measure of angle ACD? (c) What is the measure of angle DCF? (d) Label all the angle measurements. 7x – 14 = 6x + 3 (Vertical Opposites are ) - 6x + 14 - 6x + 14 x = 17 or 4x + 7 + 6x + 3 = 180 (Corresponding & Linear Pair) 10x + 10 = 180 – 10 – 10 10x = 170 10 10 x = 17 or 4x + 7 + 7x – 14 = 180 (Corresponding & Linear Pair) 11x – 7 = 180 + 7 +7 11x = 187 11 11 x = 17 One Example for finding all angles L ACD = 4(x) + 7 = 4(17) + 7 = 75 L ACD + L DCF = 180 (Linear Pairs are supplementary) 75 + L DCF = 180 - 75 - 75 L DCF = 105 4. Given: : EF || GH; AB || CD; L 1 = 35o, solve all angles. 5. Given: : || are indicated; L 1 = 108o; L 8 = 22o ; L 17 = 125o. Solve all angles below 7. Find the measure of each labeled angle. v n 50 q m u 30 120 p r 40 6. Given the following information: Solve for the value of x, y and all angles? 6y + 14 = 12y – 34 (Vertical Opposites are ) - 6y + 34 - 6y + 34 48 = 6y 6 6 y = 8 6(y) + 14 or = 12(y) – 34 6(8) + 14 = 12(8) – 34 = 62 = 62 62 + L ? = 180 (Linear Pair Ls are supplementary) - 62 - 62 L ? = 118 If L ? = 118 and L ? = 4x + 30 then 4x + 30 = 118 (Transitive Property of Equality) – 30 – 30 4x = 88 4 4 x = 22 s t Use the following picture to answer the following questions Use the following picture to answer the following questions 1) Find the measures (in degrees) of the following angles: (a) angle AFB (d) angle EFD (b) angle EFB (e) angle AFD (c) angle AFC 1) Find the measures (in degrees) of the following angles: (a) angle AFB (d) angle EFD (b) angle EFB (e) angle AFD (c) angle AFC Use the following picture to answer the following questions Use the following picture to answer the following questions 1) Find the measures (in degrees) of the following angles: (a) angle AFB (d) angle EFD (b) angle EFB (e) angle AFD (c) angle AFC 1) Find the measures (in degrees) of the following angles: (a) angle AFB (d) angle EFD (b) angle EFB (e) angle AFD (c) angle AFC Use the following picture to answer the following questions Use the following picture to answer the following questions 1) Find the measures (in degrees) of the following angles: (a) angle AFB (d) angle EFD (b) angle EFB (e) angle AFD (c) angle AFC 1) Find the measures (in degrees) of the following angles: (a) angle AFB (d) angle EFD (b) angle EFB (e) angle AFD (c) angle AFC .. Perpendicular line * Two lines are perpendicular if they intersect to form a right angle. Reflection A type of translation where the image is a mirror image flipped over the x or y axis. The image is congruent with the preimage. sum of their measures is 180 degrees. Parallel lines * Two lines are parallel if they do not intersect Translations A type of translation where the image is moved horizontally (left or right) and / or vertically (up or down). The image is congruent with the preimage, Midpoint A point that divides the segment into two congruent segments. Obtuse angle An angle with a measure more than 90 degrees. Congruent angles Two angles are congruent if they have the same measure. Segment bisector A segment, ray, line, or plane that intersects a segment at its midpoint. Transversal A line that intersects two or more coplanar lines at different points. Postulate A statement that is accepted as true without proof Coplanar Points, segments, rays or planes that are on the same plane are coplanar. Straight angle An angle with a measure of 180 degrees. Vertical angles Angle bisector A ray that divides the angle into two congruent angles. Rotation A type of translation where the image is turned about a fixed point. The image is congruent with the preimage. Theorem A statement that must be proved to be true.