PDF Name Quadrilaterals – NCERT Book Class 9th Maths Chapter 8 12 0.95 MB English
PDF PREVIEW

Introduction to Class 9th Maths Chapter 8

The Class 9th Maths Chapter 8 discusses the properties of quadrilaterals, specifically parallelograms. It covers the definition of a parallelogram, its properties, and how to prove that a shape is a parallelogram.

The chapter also introduces the Mid-point Theorem, which states that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length. The converse of this theorem is also discussed. Quadrilaterals class 9 PDF includes examples and proofs to help understand the concepts.

What will you learn from this chapter?

In this Class 9th Maths Chapter 8, you will learn about quadrilaterals, specifically focusing on parallelograms. The chapter covers the definition of a parallelogram and its properties, such as having opposite sides that are parallel and congruent. You will also learn about the relationship between diagonals and triangles within a parallelogram, including how a diagonal divides the parallelogram into two congruent triangles.

The chapter also introduces the Mid-point Theorem, which discusses the parallelism and congruence of triangles formed by connecting midpoints of sides in a triangle. The chapter includes activities, examples, and proofs to help you understand and apply these concepts.

1. What is a parallelogram and what are its defining properties?

A parallelogram is a quadrilateral with two pairs of parallel sides and opposite sides that are congruent.

How can you determine if a given quadrilateral is a parallelogram?

To determine if a given quadrilateral is a parallelogram, you can check if its opposite sides are parallel and congruent, or if its diagonals bisect each other.

What is the Mid-point Theorem and how does it relate to parallelograms?

The Mid-point Theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. This theorem can be used to prove properties of parallelograms, such as the fact that the line segment connecting the midpoints of two sides of a parallelogram is parallel to and half the length of the diagonal.

How does a diagonal divide a parallelogram into congruent triangles?

A diagonal of a parallelogram divides it into two congruent triangles.

Can you provide an example of a proof involving the properties of a parallelogram?

An example of a proof involving the properties of a parallelogram is proving that the opposite angles of a parallelogram are congruent.

How do you prove that a quadrilateral formed by connecting the midpoints of the sides of a rectangle is a rhombus?

To prove that a quadrilateral formed by connecting the midpoints of the sides of a rectangle is a rhombus, you can use the Mid-point Theorem and the properties of a rectangle.

How can you show that a line segment connecting the midpoints of two sides of a parallelogram trisects the diagonal?

To show that a line segment connecting the midpoints of two sides of a parallelogram trisects the diagonal, you can use the Mid-point Theorem and the fact that the line segment is parallel to the diagonal.

In a right-angled triangle, how can you prove that a line through the midpoint of the hypotenuse and parallel to one of the legs divides the triangle into two congruent triangles?

To prove that a line through the midpoint of the hypotenuse and parallel to one of the legs of a right-angled triangle divides the triangle into two congruent triangles, you can use the Mid-point Theorem and the properties of similar triangles.

Can you explain the relationship between the diagonals and the sides of a trapezium?

The relationship between the diagonals and the sides of a trapezium is that the diagonals of a trapezium do not have any specific relationship with its sides. Unlike in a parallelogram, where the diagonals bisect each other and have equal lengths, the diagonals of a trapezium can have different lengths and do not necessarily bisect each other. Therefore, there is no direct relationship between the diagonals and the sides of a trapezium.

Are there any special properties or theorems related to other types of quadrilaterals mentioned in this chapter?

Yes, this chapter discusses several special properties and theorems related to other types of quadrilaterals. Some of these include:-
– The properties of rectangles, such as the fact that their diagonals bisect each other and are equal.
– The properties of rhombuses, such as the fact that their diagonals bisect each other at right angles.
– The properties of squares, such as the fact that their diagonals bisect each other at right angles and are equal.
These properties and theorems provide valuable insights into the characteristics and relationships of different types of quadrilaterals.