Polygon : Types and Angles in a polygon
Subject : Mathematics
Class : JSS 2
Term : Second Term
Week : Week 4
Topic :
Polygon : Types and Angles in polygons
Previous Lesson :
Objectives:
- Students will be able to define a polygon and identify its characteristics.
- Students will be able to identify and name different types of polygons based on the number of sides they have.
- Students will be able to calculate the sum of angles in a polygon using the appropriate formula.
Materials:
- Whiteboard and markers
- Textbook with sample polygons and angles
- Rulers
- Protractors
Content ;
Polygon
A polygon is a closed figure made up of straight lines. These straight lines are called sides, and the corners where the sides meet are called vertices. Polygons can have any number of sides, but they must have at least three sides to be considered a polygon.
Types of Polygons
There are several types of polygons, and they are named based on the number of sides they have. Here are a few examples:
- Triangle: A polygon with three sides.
- Quadrilateral: A polygon with four sides.
- Pentagon: A polygon with five sides.
- Hexagon: A polygon with six sides.
- Heptagon: A polygon with seven sides.
- Octagon: A polygon with eight sides.
And so on…
Angles in Polygons
Angles are the spaces between two sides in a polygon. Each polygon has a specific number of angles based on the number of sides it has. Here are a few examples:
- Triangle: A triangle has three angles, and the sum of these angles is always 180 degrees. Each angle in a triangle is called an “angle of the triangle.”
- Quadrilateral: A quadrilateral has four angles, and the sum of these angles is always 360 degrees. Each angle in a quadrilateral is called an “angle of the quadrilateral.”
- Pentagon: A pentagon has five angles, and the sum of these angles is always 540 degrees. Each angle in a pentagon is called an “angle of the pentagon.”
- Hexagon: A hexagon has six angles, and the sum of these angles is always 720 degrees. Each angle in a hexagon is called an “angle of the hexagon.”
And so on
Sum of angles in a polygon
The sum of angles in any polygon can be calculated by using the formula:
sum of angles = (n – 2) x 180 degrees
where “n” is the number of sides in the polygon.
For example, let’s say we have a polygon with 5 sides (a pentagon). We can calculate the sum of angles in the pentagon using the formula:
sum of angles = (5 – 2) x 180 degrees sum of angles = 3 x 180 degrees sum of angles = 540 degrees
Therefore, the sum of angles in a pentagon is 540 degrees.
Similarly, for a hexagon (6 sides), the sum of angles would be:
sum of angles = (6 – 2) x 180 degrees sum of angles = 4 x 180 degrees sum of angles = 720 degrees
So, the sum of angles in a hexagon is 720 degrees.
This formula works for any polygon, whether it’s a triangle, quadrilateral, pentagon, hexagon, or any other polygon with any number of sides
The sum of the interior angles of a polygon
The sum of the interior angles of a polygon is the total measure of all the angles inside the polygon. The formula for calculating the sum of the interior angles of a polygon is:
sum of interior angles = (n – 2) x 180 degrees
where “n” is the number of sides in the polygon.
To use this formula, simply substitute the value of “n” into the formula and solve for the sum of interior angles. Here are a few examples:
Example 1: Sum of Interior Angles of a Triangle A triangle has 3 sides. Substituting “n = 3” into the formula, we get:
sum of interior angles = (3 – 2) x 180 degrees sum of interior angles = 1 x 180 degrees sum of interior angles = 180 degrees
Therefore, the sum of the interior angles of a triangle is 180 degrees.
Example 2: Sum of Interior Angles of a Quadrilateral A quadrilateral has 4 sides. Substituting “n = 4” into the formula, we get:
sum of interior angles = (4 – 2) x 180 degrees sum of interior angles = 2 x 180 degrees sum of interior angles = 360 degrees
Therefore, the sum of the interior angles of a quadrilateral is 360 degrees.
Example 3: Sum of Interior Angles of a Hexagon A hexagon has 6 sides. Substituting “n = 6” into the formula, we get:
sum of interior angles = (6 – 2) x 180 degrees sum of interior angles = 4 x 180 degrees sum of interior angles = 720 degrees
Therefore, the sum of the interior angles of a hexagon is 720 degrees.
This formula works for any polygon, whether it’s a triangle, quadrilateral, pentagon, hexagon, or any other polygon with any number of sides
Evaluation
- Which of the following is NOT a polygon? A. Triangle B. Circle C. Hexagon D. Octagon
- How many sides does a pentagon have? A. Three B. Four C. Five D. Six
- What is the sum of the interior angles in a triangle? A. 90 degrees B. 120 degrees C. 180 degrees D. 360 degrees
- A quadrilateral has how many angles? A. Two B. Three C. Four D. Five
- Which of the following polygons has the smallest sum of interior angles? A. Triangle B. Quadrilateral C. Pentagon D. Hexagon
- What is the sum of the interior angles in a hexagon? A. 360 degrees B. 540 degrees C. 720 degrees D. 900 degrees
- What is the name of a polygon with eight sides? A. Triangle B. Octagon C. Hexagon D. Pentagon
- How many sides does an octagon have? A. Six B. Seven C. Eight D. Nine
- What is the sum of the angles in a quadrilateral? A. 180 degrees B. 270 degrees C. 360 degrees D. 450 degrees
- How many angles does a triangle have? A. One B. Two C. Three D. Four
Class work
- A polygon is a closed figure made up of __________ lines. Answer: straight
- The corners where the sides of a polygon meet are called __________. Answer: vertices
- The sum of angles in a triangle is always __________ degrees. Answer: 180
- A __________ has four sides. Answer: quadrilateral
- The sum of angles in a pentagon is always __________ degrees. Answer: 540
- A polygon with seven sides is called a __________. Answer: heptagon
- The sum of the interior angles in a hexagon is __________ degrees. Answer: 720
- A polygon with six sides is called a __________. Answer: hexagon
- The formula for calculating the sum of interior angles in a polygon is (n – 2) x __________ degrees. Answer: 180
- A polygon with eight sides is called a __________. Answer: octagon
Lesson Presentation
Revision
- Revise the previous topic which was
- Angles In Mathematics
Introduction (10 minutes):
- Begin by asking the students if they know what a polygon is. Allow students to share their definitions and ideas.
- Define a polygon as a closed figure made up of straight lines, with corners where the lines meet called vertices.
- Draw an example of a polygon on the whiteboard, and ask students to identify the sides, vertices, and angles of the polygon.
Body (40 minutes):
- Introduce different types of polygons, such as triangles, quadrilaterals, pentagons, hexagons, and octagons.
- Draw examples of each type of polygon on the whiteboard and ask students to identify the number of sides and vertices in each polygon.
- Discuss the properties of each type of polygon, such as the sum of angles in a triangle always being 180 degrees, and the sum of angles in a quadrilateral always being 360 degrees.
- Hand out sample polygons and angles for students to measure with rulers and protractors, and allow them to practice calculating the sum of angles in each polygon.
Test
- What is a polygon?
- What are the corners where the sides of a polygon meet called?
- Can a polygon have curved lines? (Yes or no)
- What is the name of a polygon with three sides?
- What is the name of a polygon with five sides?
- What is the sum of angles in a triangle?
- What is the sum of angles in a quadrilateral?
- What is the name of a polygon with six sides?
- How can you calculate the sum of angles in a polygon?
- Can a triangle have a right angle? (Yes or no)
Conclusion (10 minutes):
- Review the key points of the lesson, including the definition of a polygon, different types of polygons, and how to calculate the sum of angles in a polygon using the appropriate formula.
- Encourage students to practice identifying and measuring angles in different polygons outside of class.
- Answer any remaining questions that students may have.
Assessment:
- Observe students as they work on measuring angles and calculating the sum of angles in different polygons.
- Review completed handouts to ensure students understand the material covered in the lesson.
- Assign homework that asks students to identify different polygons and calculate their sum of angles