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Transcript

What about those TRIANGLES? Triangle Application Theorems What about those ANGELS? ANGLES? Let’s check them out.... I think I’ll draw a line parallel to BC through A.... A 1 B 2 3 C What about those ANGLES? A 1 2 B What do you know now? 3 C Theorem 50 The Sum of the measures of the three angles of a triangle is 180 degrees! Finally! What do we know about exterior angles of a triangle? Which angles are exterior angles of this triangle? 1 2 B 9 8 A 7 3 4 C 6 5 How many are there? What are their remote interior angles? Exterior angle of a Polygon? O T N G S A N A X C E 1 P Y E D 2 An exterior angle of a polygon is the angle that is adjacent to and supplementary to an interior angle of the polygon. Back to Triangles.... What do we know about exterior angles of a triangle? What do we already know about the measure of each exterior angle? 2 1 3 B 9 A 8 7 C 4 6 5 What can we find out about exterior angles of a triangle? 1 A B C Theorem 51 The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Here comes a MIDLINE! B C M AB Midline M AC A A Midline is a segment that joins the midpoint of two sides of a triangle. What’s so special about a MIDLINE? Let’s investigate... Extend ED through D to a point F so that ED = DF B E A D F C Here’s the middle line.... Midline Theorem Hang on... it’s a two parter! A segment joining the midpoints of two sides of a triangle is Parallel to the third side, and Its length is one-half the length of the third side! Find x, y, and z 80 100 z 55 x y 60 Find the measure of the angle formed by the bisectors of the other two angles. (angle BEC) A 80 E B x x y y C TRAP is an isosceles trapezoid. What is the most descriptive name for the figure formed by connecting the midpoints of the sides of TRAP? R E A B D P T C B, C, D and E are midpoints of their respective sides. RECT is an rectangle. What is the most descriptive name for the figure formed by connecting the midpoints of the sides of RECT? R A E D B T C F A, B, F, and D are midpoints of their respective sides.