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What’s Your Angle? SOL 8.6 Mr. Kozar Godwin Middle School
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Unit Objectives Students will verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary angles, and complementary angles and measure angles of less than 360 degrees.
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Essential Questions How are vertical, adjacent, complementary and supplementary angles related? Adjacent angles are any 2 non-overlapping angles that share a common side and a common vertex. Vertical angles will always be nonadjacent angles. Supplementary and complementary angles may or may not be adjacent.
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Essential Questions What are the relationships between the angles formed when 2 parallel lines are cut by a transversal? When 2 parallel lines are cut by a transversal, several pairs of angles are formed. Pairs of alternate interior angles, alternate exterior angles, and vertical angles are congruent. Adjacent angles, and same side (consecutive) interior angles are supplementary.
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VOCABULARY
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Types of lines Intersecting lines Parallel lines Perpendicular lines Lines that have 1 and only 1 point in common. When 2 lines intersect, 4 angles are formed. Lines in the same plane and never intersect. Same distance apart. Lines that intersect at right angles. 90 degrees
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There are four main types of angles. Straight angle Right angle Acute angle Obtuse angle A B C A B C A B C BA C Types Of Angles
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Protractor is used to measure and draw angles. Angles are accurately measured in degrees. Measurement Of An Angle
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Right angle: An angle whose measure is 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle
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Obtuse angle: An angle whose measure is greater than 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle
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Acute angle: An angle whose measure is less than 90 degrees. Right AngleAcute AngleStraight AngleObtuse Angle
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Straight angle: An angle whose measure is 180 degrees. Right AngleAcute AngleStraight AngleObtuse Angle
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Pairs Of Angles : Types Adjacent angles Vertically opposite angles Complimentary angles Supplementary angles Linear pairs of angles Two angles that have a common vertex and a common ray Opposite angles Sum of two angles is 90 0 Sum of two angles is 180 0 Two adjacent supplementary angles
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Two angles that have the same measure are called congruent angles. Congruent angles have the same size and shape. A B C 30 0 D E F D E F Congruent Angles
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Adjacent Angles Two angles that have a common vertex and a common ray are called adjacent angles. C D B A Common ray Common vertex Adjacent Angles ABD and DBC Adjacent angles do not overlap each other. D E F A B C ABC and DEF are not adjacent angles
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Non-Adjacent Angles Do NOT share a common side.
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Vertically Opposite Angles Vertically opposite angles are pairs of angles formed by two lines intersecting at a point. APC = BPD APB = CPD A D B C P Four angles are formed at the point of intersection. Point of intersection ‘P’ is the common vertex of the four angles. Vertically opposite angles are congruent.
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If the sum of two angles is 90 0, then they are called complimentary angles. 60 0 A B C 30 0 D E F ABC and DEF are complimentary because 60 0 + 30 0 = 90 0 ABC + DEF Complimentary Angles
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If the sum of two angles is 180 0 then they are called supplementary angles. PQR and ABC are supplementary, because 100 0 + 80 0 = 180 0 R Q P A B C 100 0 80 0 PQR + ABC Supplementary Angles
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Transversal A line that intersects two or more coplanar lines in different points forming eight (8) angles. Interior angles lie between 2 lines
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Alternate Interior Angles < 3 & < 6 < 4 & < 5 < 4 & < 6 < 3 & < 5 Same Side Interior Angles Alternate exterior lie outside the 2 lines < 1 <8 <2 <7
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Reflex Angles Measure more than 180 degrees but less than 360 degrees.
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