1-4. Study Guide and Intervention. Angle Measure

Transcription

1 IO 1-4 tudy Guide and Intervention ngle easure easure ngles If two noncollinear rays have a common endpoint, they form an angle. he rays are the sides of the angle. he common endpoint is the vertex. he angle at the right can be named as,,, or 1. right angle is an angle whose measure is 90. n acute angle has measure less than 90. n obtuse angle has measure greater than 90 but less than xample 1 xample 2 lassify each angle as right, acute, or obtuse. hen use a protractor to measure the angle to the Q nearest degree. opyright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. a. ame all angles that have as a vertex. hree angles are 1, 2, and 3. For other angles, use three letters to name them: Q,, and. b. ame the sides of 1., efer to the figure at the right. 1. ame the vertex of ame the sides of. 3. Write another name for. a. Using a protractor, m = < 90, so is an acute angle. b. Using a protractor, m = > 115 > 90, so is an obtuse angle. c. lassify each angle as right, acute, or obtuse. hen use a protractor to measure the angle to the nearest degree. 4. Using a protractor, m = 90. is a right angle Lesson hapter 1 25 Glencoe Geometry

2 IO 1-4 tudy Guide and Intervention (continued) ngle easure ongruent ngles ngles that have the same measure are congruent angles. ray that divides an angle into two congruent angles is called an angle bisector. In the figure, is the angle bisector of. oint lies in the interior of and. xample efer to the figure above. If m = 2x + 14 and m = x + 34, find x and find m. ince bisects,, or m = m. 2x + 14 = x + 34 m = 2x x x = x x = 2(20) + 14 x + 14 = 34 = x = = 54 x = 20 LG In the figure Q and Q are opposite rays. Q bisects Q. 1. If m Q = 60 and m Q = 4x + 14, find the value of x. Q 2. If m Q = 3x + 13 and m Q = 6x - 2, find m Q. LG In the figure and are opposite rays. F bisects. 3. If m F = 6x + 4 and m F = 7x - 2, find m F If m 3 = 4x + 10 and m 4 = 5x, find m If m 3 = 6y + 2 and m 4 = 8y - 14, find m. 6. Let m 1 = m 2. If m = 100 and m = 2(r + 5), find r and m. F opyright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. hapter 1 26 Glencoe Geometry

3 IO 1-5 tudy Guide and Intervention ngle elationships airs of ngles djacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points. pair of adjacent angles with noncommon sides that are opposite rays is called a linear pair. Vertical angles are two nonadjacent angles formed by two intersecting lines. xample ame an angle or angle pair that satisfies each condition. a. two vertical angles FI and GFH are nonadjacent angles formed by two intersecting lines. hey are vertical angles. b. two adjacent angles and have a common vertex and a common side but no common interior points. hey are adjacent angles. c. two supplementary angles FG and GFH form a linear pair. he angles are supplementary. d. two complementary angles m + m = 90. hese angles are complementary. opyright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. ame an angle or angle pair that satisfies each condition. 1. two adjacent angles 2. two acute vertical angles 3. two supplementary adjacent angles an angle supplementary to For 5 7, use the figure at the right. 5. Identify two obtuse vertical angles. 6. Identify two acute adjacent angles. V U 7. Identify an angle supplementary to U. 8. Find the measures of two complementary angles if the difference in their measures is 18. L Lesson 1-5 hapter 1 31 Glencoe Geometry

4 IO 1-5 tudy Guide and Intervention (continued) ngle elationships erpendicular Lines Lines, rays, and segments that form four right angles are perpendicular. he right angle symbol indicates that the lines are perpendicular. In the figure at the right, is perpendicular to, or. xample If Z Z, then m Z = 90. m ZQ + m QZ = m Z Find x so that Z and Z are perpendicular. um of parts = whole (9x + 5) + (3x + 1) = 90 ubstitution 12x + 6 = 90 12x = 84 ombine like terms. ubtract 6 from each side. x = 7 ivide each side by 12. Q (9x + 5) (3x + 1) Z 1. Find the value of x and y so that Q. 2. Find m. 3. m F = 3x + 10, m = x, and F. Find the value of x. 4. If m F = 7y - 3 and m F = 3y + 3, find the value of y so that. 5. Find the value of x, m Q, and m Q. 6. Find the value of y, m, and m W. 5x x (9y + 18) Q F 3x (8x + 2) Q (4y - 5) (2y + 5) W V opyright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. hapter 1 32 Glencoe Geometry

5 IO 1-6 tudy Guide and Intervention (continued) wo-imensional Figures erimeter, ircumference, and rea he perimeter of a polygon is the sum of the lengths of all the sides of the polygon. he circumference of a circle is the distance around the circle. he area of a figure is the number of square units needed to cover a surface. xample Write an expression or formula for the perimeter and area of each. Find the perimeter and area. ound to the nearest tenth. a. 3 in. a 4 in. b c 5 in. b. 3 ft l 2 ft w l w c. 5 in. r = a + b + c = = 12 in. = 1 2 bh = 1 2 (4)(3) = 6 in 2 = 2l + 2w = 2(3) + 2(2) = 10 ft = lw = (3)(2) = 6 ft 2 = 2πr = 2π(5) = 10π or about 31.4 in. = πr 2 = π(5) 2 = 25π or about 78.5 in 2 Find the perimeter or circumference and area of each figure. ound to the nearest tenth cm 14 yd 3 cm 2 cm 3.5 cm OOI GOY Graph each figure with the given vertices and identify the figure. hen find the perimeter and area of the figure. 5. ( 2, 4), (1, 3), (4, 4) 6. X( 3, 1), Y( 3, 3), Z(4, 1), (4, 2) y cm 4 ft 4 cm y 5 cm opyright Glencoe/cGraw-Hill, a division of he cgraw-hill ompanies, Inc. x x hapter 1 38 Glencoe Geometry