"Sum of Interior Angle and Sum of Exterior Angle of Polygon" PPT

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"Sum of Interior Angle and Sum of Exterior Angle of Polygon" PPT

Part One: Guess

Xiao Ming has an idea:

The 2008 Olympic Games will be held in Beijing. It would be meaningful if we could design a polygonal flower bed whose interior angles sum to 2008°! Can Xiao Ming’s idea be realized?

learning target:

1. Understand the definition of polygon and the concepts of polygon’s vertices, sides, interior angles, exterior angles and diagonals.

2. Explore methods to find the sum of interior angles and exterior angles of polygons

3. Be able to apply the formulas of sum of interior angles and sum of exterior angles of polygons to solve problems

The sum of interior angles and the sum of exterior angles of polygons PPT, Part 2: Polygons

On a plane, a figure composed of line segments that are not on the same straight line and connected end to end is called a polygon.

Diagonal: The line segment connecting two non-adjacent vertices of a polygon is called the diagonal of a polygon.

Explore research

Use triangle knowledge to explore how many degrees the sum of the interior angles of a quadrilateral equals? How many ways can you think of?

activity plan

1. Work in a group of four to complete the segmentation of the quadrilateral on paper.

2. Explore the sum of the interior angles of a quadrilateral obtained by different division methods.

Precautions

1. Use a ruler to draw, and the dividing lines are represented by dotted lines "----".

2. Come up with as many different methods as possible to find the sum of its interior angles.

Sum of interior angles and sum of exterior angles of polygons PPT, Part 3 content: Sum of interior angles of polygons

The sum of the interior angles of an n-sided polygon is equal to (n-2)×180° (n≥3)

Starting from one vertex of an n-sided polygon, (n-3) diagonals can be drawn

Then an n-sided polygon with n vertices has n(n-3)/2 diagonals.

Example: Find the measure of the sum of the interior angles of a pentagon.

Solution: (n-2)×1800

=(15-2)×1800= 23400

Answer: The sum of the interior angles of a pentagon is 23400

Consolidation exercise one:

1. The sum of the interior angles of a heptagon is ( )

2. The sum of the interior angles of a seventeen-sided polygon is ( )

3. The sum of the interior angles of an octagon is ( )

Consolidation exercise two:

1. If the sum of the interior angles of a polygon is 1260°, it is a polygon ( ).

2. If the sum of the interior angles of a polygon is 1800°, it is a polygon ( ).

Consolidation exercise three:

1. There are ( ) diagonals in a decagon.

2. An n (n≥3) polygon has ( ) diagonals starting from a vertex.

The sum of the interior angles and the sum of the exterior angles of a polygon PPT, Part 4: The sum of the exterior angles of a polygon

The sum of the exterior angles of a polygon is 360°

Example: Given a polygon, the sum of its interior angles is equal to the sum of its exterior angles. Please indicate how many sides this polygon has.

Solution: Suppose the number of sides of a polygon is n, then the sum of its interior angles is equal to (n-2)×180°, and the sum of its exterior angles is equal to 360°. From (n-2)×180°= 360°, the solution is n=4. So this polygon is a quadrilateral.

For example: As shown in the figure, Xiaoliang starts from point O, goes forward 5m and then turns right 20°, and after going 5m forward turns right 20° again, and walks n times in this way to exactly return to point O.

(1) What is the degree of each interior angle of the n-sided polygon that Xiaoliang walked out of? What is the sum of the interior angles?

(2) What is the perimeter of the n-gon that Xiaoliang walked out of?

The sum of interior angles and the sum of exterior angles of polygons PPT, Part 5: Apply what you learn

1. Xiao Ming has an idea:

The 2008 Olympic Games will be held in Beijing. It would be meaningful if we could design a polygonal flower bed whose interior angles sum to 2008°! Can Xiao Ming’s idea be realized?

2. For the template as shown in the figure, the extension lines of AB and CD intersect at an angle of 80° according to the regulations. Since the intersection point is not on the board, it is inconvenient to measure. The quality inspector measured ∠BAE=122° and ∠DCF=155°. If you are a quality inspector, how do you know if the template is qualified? Why?

Classroom testing:

1. The sum of the interior angles of a decagon is equal to _______.

2. If each exterior angle of a polygon is equal to 30°, then the polygon is a ______ polygon.

3. A polygon whose interior angles sum to 1440° is ______.

4. A polygon whose sum of interior angles is equal to the sum of exterior angles is a ______ polygon.

5. In pentagon ABCDE, if ∠A = ∠D = 90°, ∠B:∠C :∠E = 3:8:7, find the degrees of ∠B, ∠C and ∠E.

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, sum of interior angles and sum of exterior angles of polygons PPT download, .PPT format;

For more information about the PPT courseware "Sum of Interior Angle and Sum of Exterior Angle of Polygon", please click the PPT tab of "Sum of Interior Angle and Sum of Exterior Angle of Polygon".

"Sum of Interior Angle and Sum of Exterior Angle of Polygon" Parallelogram PPT (Lesson 2):

"Sum of Interior Angle and Sum of Exterior Angle of Polygon" Parallelogram PPT (Lesson 2), 24 pages in total. Learning objectives: Understand and master the derivation process of the sum of exterior angles theorem of polygons; be able to comprehensively apply the sum of interior angles and sum of exterior angles theorem of polygons. ... ... ... Pre-learning 1..

"Sum of Interior Angle and Sum of Exterior Angle of Polygon" Parallelogram PPT (Lesson 1):

"Sum of interior angles and sum of exterior angles of polygons" Parallelogram PPT (Lesson 1), 23 pages in total. Learning objectives: Explore the sum formula of the interior angles of polygons and further develop reasoning skills; master the sum formula of the interior angles of polygons, and be able to use the formulas to solve practical problems. ... ... ....

"Sum of interior angles and sum of exterior angles of polygons" PPT courseware:

"The sum of interior angles and the sum of exterior angles of polygons" PPT courseware Part 1: Polygon In a plane, a closed figure composed of several line segments that are not on the same straight line connected end to end is called a polygon. Diagonal: In a polygon, connects two non-adjacent vertices..

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Update Time: 2024-07-29

This template belongs to Mathematics courseware Hebei Education Edition Eighth Grade Mathematics Volume 2 industry PPT template

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