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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.

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Presentation on theme: "8.1 – Lines and Angles Defn: Space: The region that extends in all direction indefinitely. Plane: A flat surface without thickness that extends indefinitely."— Presentation transcript:

1 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..

2 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

3 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

4 8.1 – Lines and Angles Identify each of the following figures. VE YI CF  SBT  TBS  B  VHT  THV  H

5 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?

6 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°.

7 8.1 – Lines and Angles Classifying Angles straightacuteobtuse right obtuse

8 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°

9 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?

10 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

11 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

12 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°

13 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

14 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

15 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°

16 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°

17 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

18 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

19 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

20 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 =

21 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

22 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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