Geometry Angles: Interior and Exterior Polygon Angle Sums
Explore the properties of interior and exterior angles in polygons, including finding the sum of interior angles for various shapes, determining the number of sides in a polygon given the sum of angles, and making conjectures on angle sums without measuring. Delve into the relationship between the number of sides and angle measures in polygons.
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Presentation Transcript
Bell work: Find the range of possible values for each variable 6, 6, and x as the side lengths of a triangle
6-1: The Polygon Angle Sum Theorem
Partner Work With a partner, determine the total sum of the interior angles for a square, a hexagon, and an octagon (4, 6, and 8 sides). You can do this by measuring, estimating, or any other method you d like, but be prepared to justify your answer. Once you ve done this, make a conjecture (without drawing or measuring) on the sum of the angles of a decagon (10 sides)
What is the sum of the interior angles of a heptagon? (7 sides) What is the sum of the interior angles of a 17-gon?
The sum of all the interior angles of a polygon is 1980 how many sides does the shape have?
What is the sum of the interior angles of a 35-gon? How many sides does the polygon with interior angle sum equal to 2880 have?
Notes Theorem 6.1: The sum of the measures of all the interior angles of a polygon with n- sides is (n-2) x 180 degrees An Equilateral Polygon has all sides equal An Equiangular Polygon has all angles equal A Regular Polygon is equilateral and equiangular
Find the measure of one interior angle to the regular polygon
What would the total sum of the EXTERIOR angles for a square, a pentagon, and a hexagon (4, 5, and 6 sides) be?. You can do this by measuring, estimating, or any other method you d like, but be prepared to justify your answer. Once you ve done this, make a conjecture (without drawing or measuring) on the sum of the angles of a decagon (10 sides)
Notes Corollary to theorem 6.1: The measure of each interior angle of a REGULAR n-gon = ? Theorem 6.2: The sum of the measures of the exterior angles of any polygon is 360 ? 2 180
What is the measure of each interior angle in a regular hexagon? What is the measure of each interior angle in a regular nonagon?
What is the sum of the measures of the exterior angles of a 225-gon? Find the measures of an interior angle and an exterior angle for a regular dodecagon (12 sides)
One row at a time, get a white board, marker, and eraser from the front of the class Show your work for all problems Any non-math related drawings will result in a loss of whiteboard privileges
Vocab Perpendicular Bisector Angle Bisector Median Altitude Circumcenter Incenter Centriod Orthocenter Midsegment
Draw 3 triangles now, construct an altitude, median, and circumcenter, one in each triangle (and identify it)
List the sides of the triangle from shortest to longest.
Homework Study for a chapter 5 quiz on Friday Section 6.1, page 356-357: 7, 10, 12, 16, 20, 23 Honors: Add 11, 17, 29, 32,
