Informal Geometry 10.2 Diagonals and Angle Measure.

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Presentation transcript:

Informal Geometry 10.2 Diagonals and Angle Measure

Diagonals A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Ex. 1. How many diagonals can we draw in the rectangle?

Triangles Ex. 2. How many diagonals can be drawn in the triangle?

What is the sum of the interior angles of a triangle? Ex. 3. Find the missing angles. 3xº xº 72º A BC m<A = m<B =

Quadrilaterals… Draw all possible diagonals from Vertex A. How many triangles were formed as a result? What do you think this means for the sum of the interior angles of a quadrilateral? A

Polygons Hexagon Nonagon Octagon Decagon

INTERIOR ANGLE SUM S I = (n – 2) 180º n = number of sides Ex. 4. Find the sum of the interior angles of a convex octagon. Ex. 5. Find the sum of the interior angles of a convex 15-gon.

Regular Polygons A REGULAR polygon is Equilateral and Equiangular (all sides and all angles ). To Find the measure of each Interior Angle of a regular convex polygon. º

Ex. 6. Find the measure of each angle in a regular convex octagon.

Exterior Angles The Exterior Angle of any polygon forms a linear pair with an Interior angle of a polygon. Ex. <1 is an exterior angle. <1 and <2 form a linear pair. <1 <2 m<1 + m<2 = 180º

Sum of the exterior angles of a convex polygon. 360º ALL Exterior Angles of EVERY polygon add up to 360º

Ex. 7. What is the sum of the exterior angles of a convex triangle? Ex. 8. What is the sum of the exterior angles of a convex 300-gon?

Regular Polygons To Find the measure of each Exterior Angle of a regular convex polygon, find

Ex. 9. Find the measure of each exterior angle of a regular heptagon. Ex. 10. The measure of each exterior angle of a regular polygon is 40º. How many sides does it have?

Homework Page 411: 4-25all