Bell work: Find the range of possible values for each variable

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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 = 𝑛−2 180 𝑛 Theorem 6.2: The sum of the measures of the exterior angles of any polygon is 360

What is the measure of each interior angle in a regular hexagon? What is the measure of each interior angle in a regular nonagon?

Find the measure of angle Y

Find the measure of angle G

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)

Chapter 5 Review

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 Circumcenter Incenter 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.

Find the value of X

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,