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8.1 – Lines and Angles Defn: Space: The region that extends in all direction indefinitely. Plane: A flat surface without thickness that extends indefinitely in two directions..

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8.1 – Lines and Angles Defn: Ray: A part of a line with one end point extending indefinitely in one direction. A Line: A set of points extending indefinitely in opposite directions. Line Segment: A piece of a line that has two end points. B Line AB Line AB A B line segment AB AB A B ray ABAB

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8.1 – Lines and Angles Defn: Angle: A two dimensional plane whose sides consist of two rays that share the same end point. The shared point is called the vertex. Angle BAC A B x C BAC Angle CAB CAB Angle A A Angle x x

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8.1 – Lines and Angles Identify each of the following figures. VE YI CF SBT TBS B VHT THV H

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8.1 – Lines and Angles Use the given figure to answer the questions. BAC CAB A AEC CEA E What are the name(s) of the given angle? 1 1 What are the other names of angle x?

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8.1 – Lines and Angles Classifying Angles Right angle: Any angle that measures 90°. Degree: A unit for measuring angles. The symbol denoting degrees is a raised circle (45°). Straight angle: Any angle that measures 180° (a straight line). Acute angle: Any angle whose measurement is between 0° and 90°. Obtuse angle: Any angle whose measurement is between 90° and 180°.

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8.1 – Lines and Angles Classifying Angles straightacuteobtuse right obtuse

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8.1 – Lines and Angles Special Pairs of Angles What is the compliment of 15°? Complimentary angles: Two angles whose sum is 90°. They are compliments of each other. Supplementary angles: Two angles whose sum is 180°. They are supplements of each other. What is the supplement of 80°? 90 – 15 =75°180 – 80 = 100° What is the supplement of 95°? 180 – 95 = 85° What is the compliment of 29°? 90 – 29 =61° What is the supplement of 29°? 180 – 29 = 151°

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8.1 – Lines and Angles Calculating the Measure of an Angle What type of angle is 57°? Given the figure below, what is the measure of 1? acute 68 – 23 = What type of angle is 45°? acute 45° 68° 23° 176 – 119 =57° 119° 176° Given the figure below, what is the measure of CPD?

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8.1 – Lines and Angles Lines in a Plane 1 = 3 Intersecting Lines: Lines in a plane that cross at a common point. If two lines intersect, they create four angles. Vertical angles: Of the four angles formed from two intersecting lines, these are the two pairs of opposite angles. The measures of the opposite angles are the same 2 = 4

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8.1 – Lines and Angles Lines in a Plane Parallel lines: Two or more lines in a plane that do not intersect. Perpendicular lines: Two lines in a plane that intersect at a 90° angle. line l line 2 1 line 3 line 4 3 4

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8.1 – Lines and Angles Lines in a Plane 1 + 2 = 180° Adjacent angles: Angle that share a common side. Adjacent angles formed from two intersecting lines are supplementary DBC is adjacent to CBA as they share the common side BC. 2 + 3 = 180° 3 + 4 = 180° 4 + 1 = 180°

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8.1 – Lines and Angles Lines in a Plane Transversal lines: Any line that intersects two or more lines at different points. The position of the angles created by the transversal line have specific names a b c d e f g h Corresponding angles: a & e, b & f, d & h, and c & g Alternate interior angles: d & f and c & e

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8.1 – Lines and Angles Lines in a Plane If two parallel lines are cut by a transversal, then: 1 a b c d e f g h (a) The corresponding angles are equal, (b) The alternate interior angles are equal. Corresponding angles: a = e, b = f, Alternate interior angles: d = f and d = h, and c = g c = e

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8.1 – Lines and Angles Given the measure of one angle, calculate the measures of the other angles. m 1 = 30° m 2 = m 3 = m 4 = 30° 180 – 30 = 150° m 4 = 127° m 1 = m 2 = m 3 = 53° 180 – 127 = 127° 53°

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8.1 – Lines and Angles 1 a b c d e f g h Given the measure of one angle, calculate the measures of the other angles. m e = 98° m a = m b = m c = 82° 98° m d = m f = m g = m h = 98° 180 – 98 = 82°

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Perimeter: The perimeter of any polygon is the total distance around it. The sum of the lengths of all sides of the polygon is the perimeter. Defn. 8.2 – Perimeter Calculate the perimeter of each of the following: The length of a rectangle is 32 centimeters and its width is 15 centimeters. P = = 94 cm P = 2(32) + 2(15) =94 cm

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8.2 – Perimeter Calculate the perimeter of each of the following: The figure is a rectangle with the given measurements. P = =45 ft P = 2(18) + 2(10) = 56 m 18 meters 10 meters = 15 feet 7 feet 9 feet 14 feet

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8.2 – Perimeter Calculate the perimeter of each of the following: All angles in the figure are 90°. P = = in 22 inches 17 inches inches 29 inches 29 – 12 =17 inches =39 inches

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A rectangular lot measures 60 feet by 120 feet. Calculate the cost of a fence to be installed around the perimeter of the lot if the fence costs $1.90 per foot. 8.2 – Perimeter Calculate the perimeter. Calculate the cost of the fence. C = 360 · 1.90 $ = P = 2(60) + 2(120) =360 ft =

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Blue line = Diameter Red line = Radius d = 2r Circumference – the length around the edge of a circle. C = d r d C = 2 r or 8.2 – Perimeter

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Find the exact circumference of a circle whose diameter is 20 yards yds x decimal places C = dC = 2 r or C = 3.14 (20) 8.2 – Perimeter Find the approximate value of the circumference of a circle whose diameter is 7 meters. ( Use 3.14 as an approximation of .) C = d C = 20 C = 20 yds C = d

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