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Transcript
3.5-3.8 By: Alex Melnick and Brian Yoon 3.5 – Triangle Sum Theorem • The Parallel Postulate – Given a line and a point not on the line, there is one and only one line that contains the give point and is parallel to the given line • Triangle Sum Theorem – The sum of the measures of the angles of a triangle is 180° Given: C 4 1 5 ABC Prove: angle 1 + angle 2 + angle 3 =180° Statement ABC 2 A L // AB 3 B angle1+ angle4 + angle5 = 180° angle 2 = angle 4 angle 3 = angle 5 Reason Given Parallel Postulate 3 angles form a line 3.6-Angles in polygons Polygon Types: Concave-1 or more angles are pointed inwards Convex- All angles face outwards. Shape Sides Sum of interior angles One interior angle Triangle 3 180 60 Square 4 360 90 Pentagon 5 540 108 Hexagon 6 720 120 Heptagon 7 900 128.6` Octagon 8 1080 135 N-gon N 180(N-2) 180(N-2) N The sum of the exterior angles of all polygons are 360 3.7- Mid-segments of triangles and trapezoids 3.8 Analyzing Polygons With Coordinates • Definition of slope – The slope of a nonvertical line that contains the points(x1, y1) and (x2, y2)is equal to y2-y1 x2-x2 Ex. Find the slope of AB with the endpoints A(5,-3) and B(2,3) y2-y1 x2-x1 3 – (-3) 2–5 6 -3 3.8 cont. Parallel and Perpendicular Lines • Parallel Line Theorem – Two nonvertical lines are parallel if and only id they have the same slope. Any two vertical lines are parallel • Perpendicular Lines Theorem – Two nonvertical lines are perpendicular if and only if the product of their slopes is 1. Any vertical line is perpendicular to any horizontal line Midpoint Formula • The Midpoint of a segment with endpoints (x1, y1) and (x2, y2) has the following coordinates: Quiz • The sum of the angles in a regular polygon is 34,020°, how many sides does the polygon have? • 191 • If one angle of a right triangle is 86 what are the measurements of the other two angles? • 4° and 90° • The base of a triangle is 279.36 and a segment that is inside of the triangle is 138.18, is this the midsegment? • No. More Math Fun: HERE!! THE END =(