Chapter 9: Basic Polygons
What you need to learn in this chapter
In this chapter, we will be learning about basic polygons. We will start by understanding the relationship between the number of sides, vertices, and diagonals of polygons. We will also learn how to draw polygons, label their vertices, and name them based on the labeled vertices.
Next, we will explore the properties of triangles. We will recognize and list the geometric properties of different types of triangles, which will help us classify them. We will also make and verify conjectures about the sum of interior angles, the sum of interior angle and adjacent exterior angle, and the relation between exterior angle and the sum of the opposite interior angles of a triangle.
Moving on, we will study the properties of quadrilaterals. We will describe the geometric properties of various types of quadrilaterals and classify them based on these properties. We will also make and verify conjectures about the sum of interior angles of a quadrilateral, the sum of interior angle and adjacent exterior angle of a quadrilateral, and the relationship between the opposite angles in a parallelogram.
By the end of this chapter, we will have a solid understanding of polygons, triangles, and quadrilaterals, and be able to apply their properties to solve mathematical problems.
Topics in this chapter
1. Polygons
What you will learn in this topic
- State the relationship between the number of sides, vertices and diagonals of polygons.
- Draw polygons, label vertices of polygons and name the polygons based on the labeled vertices.
2. Properties of triangles and the interior and exterior angles of triangles
What you will learn in this topic
- Recognise and list geometric properties of various types of triangles. Hence classify triangles based on geometric properties.
- Make and verify conjectures about (i) the sum of interior angles, (ii) the sum of interior angle and adjacent exterior angle, (iii) the relation between exterior angle and the sum of the opposite interior angles of a triangle.
- Solve problems involving triangles.
3. Properties of quadrilaterals and the interior and exterior angles of quadrilaterals
What you will learn in this topic
- Describe the geometric properties of various types of quadrilaterals. Hence classify quadrilaterals based on the geometric properties.
- Make and verify the conjectures about (i) the sum of interior angles of a quadrilateral, (ii) the sum of interior angle and adjacent exterior angle of a quadrilateral, and (iii) the relationship between the opposite angles in a parallelogram.
- Solve problems involving quadrilaterals.
- Solve problems involving the combinations of triangles and quadrilaterals.
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