Sections 3.5-3.8 GEOMETRY ROCKS! Sydney, Alex, and Julia!!!!

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Presentation transcript:

Sections GEOMETRY ROCKS! Sydney, Alex, and Julia!!!!

3.5 Triangle Sum Theorem The sum of the interior angles of any triangle is equal to 180 degrees. <1+<2+<3= 180

3.5 Parallel Postulate Given a line and a point not on the line, there is one and only one line that contains the given point and is parallel to the given line. The measure of the exterior angle of a is equal to the sum of the two remote interior angles 3.5 Exterior Angle Theorem <1=<2+<3

Angles in Polygons! 3.6 Sides Sum of Interior <‘s1 < (2x180) 90

3.6 Sides Sum of interior <‘s 1<

3.6 Sides Sum of interior < ‘ s 1< n 1080(n-2) 180(n-2) n n-gon

3.6 **Sum of Exterior Angles** It DOES NOT matter what the shape is, the sum of the EXTERIOR angles is 360° Sum of exterior angles = 360 °

3.7 CAN YOU FIND THE MIDDLE? Mid-segment= segment whose end points are the midpoints of two sides –Mid-segment of a is ll to a side of the and has a measure = to ½ that side –Mid-segment of a trapezoid is ll to the bases of the trapezoid and has a measure equal to ½(Base 1 + Base 2) mn A C B Segment MN is ll to and ½ the length of AC A BC D m n Length of MN is ½ the sum of AB+DC

3.7 USE YOUR BRAIN! Find the measures: 2x+2 6x-8 A B C HINT: to find the answer, set up the following equation ½ (6x-8) = 2x+ 4

3.8 PPPPPOLLLLYGONS These are HANDY DANDY formulas: Slope: measures steepness of a line y 2 - y 1 X 2 -X 1 Midpoint: ( x1+x2, y1+y2) 2 2 Test triangle mid-segment conjecture: Draw ABC A(3,6) B(1,0) C(5,0) Hint: find midpoint of AB and AC to find mid-segment of ABC A BC