Designed by Dave Meyer. All rights reserved Tutorial 5a.

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Presentation transcript:

Designed by Dave Meyer. All rights reserved Tutorial 5a

Designed by Dave Meyer. All rights reserved Polygon -- A union of segments that meet only at endpoints. 1.

Designed by Dave Meyer. All rights reserved The following are not Polygons... a) b) because a polygon consists entirely of segments. because in a polygon only consecutive sides intersect and only at endpoints A BC D EF 2.

Designed by Dave Meyer. All rights reserved The following are not Polygons c) d) cont... P R O NS D LQ T because each vertex must belong to exactly 2 sides (vertex P belongs to 3). because each segment must meet exactly two other segments.

Designed by Dave Meyer. All rights reserved Parts of Polygons polygon ABCDEF Vertices: A, B, C, D, E, F F A B C D E 3.

Designed by Dave Meyer. All rights reserved Parts of Polygons polygon ABCDEF Vertices: A, B, C, D, E, F F A B C D E Sides: AB, BC, CD... 3.

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD polygon ABCDEF Vertices: A, B, C, D, E, F

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD polygon ABCDEF Vertices: A, B, C, D, E, F

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD polygon ABCDEF Vertices: A, B, C, D, E, F

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD... Diagonal -- A segment joining 2 nonadjacent vertices. 3. polygon ABCDEF Vertices: A, B, C, D, E, F

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD... Diagonals AC, BE, CF polygon ABCDEF Vertices: A, B, C, D, E, F

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD... Diagonals AC, BE, CF polygon ABCDEF Vertices: A, B, C, D, E, F

Designed by Dave Meyer. All rights reserved Parts of Polygons F A B C D E Sides: AB, BC, CD... Diagonals AC, BE, CF polygon ABCDEF Vertices: A, B, C, D, E, F

Types of Polygons A polygon is convex if no diagonal contains points outside the polygon. A polygon is concave if a diagonal contains points outside the polygon. A E D Y T D F H M N Q 4.

Designed by Dave Meyer. All rights reserved Convex polygon -- A polygon where all of its diagonals fall on the inside of the figure. Which polygon is convex? Click on your choice. AB C DE QR S TU V 4. cont...

Designed by Dave Meyer. All rights reserved Regular Polygon -- A convex polygon with all of its sides congruent and all angles congruent. QR S TU V 4. cont...

Designed by Dave Meyer. All rights reserved Names of Polygons triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon icosagon Number of sides Name

Designed by Dave Meyer. All rights reserved Finding the sum of the angles of a polygon (n - 2)180 (5 - 2)180 = (3)180 = 540 The sum of the measures of the interior angles of a polygon is (n - 2)180. Where n represents the number of sides. The sum of all 5 angles in this polygon is 540º 6.

Designed by Dave Meyer. All rights reserved ApplicationsApplications Find the sum of the interior angles of a: pentagon decagon quadrilateral 6. (n - 2)180 Click the button below to check your answers! cont...

Designed by Dave Meyer. All rights reserved ApplicationsApplications Find the sum of the interior angles of a: pentagon decagon quadrilateral 540º 1440º 360º 6. (n - 2)180 Click on the answer to see the problem worked out! cont...

Designed by Dave Meyer. All rights reserved If a polygon has angles with a sum of 720 then how many sides does the polygon have? If a polygon has angles with a sum of 720 º then how many sides does the polygon have? (n - 2)180 = n = n = 1080 n = 6 The polygon has 6 sides! 7.

Designed by Dave Meyer. All rights reserved ApplicationsApplications How many sides does a polygon have if the sum of the measures of its interior angles is: 720? 1440? 2700? (n-2)180 = 720 ; n = 6 sides (n-2)180 = 1440; n = 10 sides (n-2)180 = 2700; n = 17 sides 7. (n - 2)180 cont...

Designed by Dave Meyer. All rights reserved More Applications (n - 2)180 (6 - 2)180 = = ¸ If the sum of the first five interior angles of a hexagon is 700, find the measure of the sixth angle. cont... The six angle measures 20º

Designed by Dave Meyer. All rights reserved Regular Polygon: A polygon that is both equiangular and equilateral regular polygon What’s the formula to find the measure of each angle of a regular polygon? (n - 2)180 n 8.

Designed by Dave Meyer. All rights reserved ApplicationsApplications (n - 2)180 n 8.  Find the measure of each interior angle of a regular hexagon cont... (6 - 2)180 6 = = 120º 120º

Designed by Dave Meyer. All rights reserved ApplicationsApplications (n - 2)180 n 8.  Each interior angle of a regular polygon measures 135. Find the number of sides that the polygon has. cont... = 135 (n - 2)180 = 135n 180n = 135n = - 45n 8 = n

Designed by Dave Meyer. All rights reserved Exterior Angles The of a polygon The sum of the exterior angles of a polygon is 360 Each exterior angle of a regular polygon is 360 n

Designed by Dave Meyer. All rights reserved SummarySummary   The sum of the interior angles of a polygon is (n - 2)180   Each angle of a regular polygon measures (n - 2)180 n   The sum of exterior angles is 360   Each exterior angle of a regular polygon is 360 n

Designed by Dave Meyer. All rights reserved Time to move on to the assignment or the next lesson.

Designed by Dave Meyer. All rights reserved ApplicationsApplications Find the sum of the interior angles of a: pentagon A pentagon has 5 sides; So- (n – 2)180 = (5 – 2)180 = (3)180 = 540º 6. (n - 2)180 cont... Back

Designed by Dave Meyer. All rights reserved ApplicationsApplications Find the sum of the interior angles of a: decagon A decagon has 10 sides; So- (n – 2)180 = ( 10 – 2 ) 180= (7)180 = 1440º 6. (n - 2)180 cont... Back

Designed by Dave Meyer. All rights reserved ApplicationsApplications Find the sum of the interior angles of a: quadrilateral A quadrilateral has 4 sides; So- (n – 2)180 = (4 – 2)180 = (2)180 = 360º 6. (n - 2)180 cont... Back