# How do you prove a quadrilateral is a parallelogram Class 9?

## How do you prove a quadrilateral is a parallelogram Class 9?

– If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. – Diagonal of a parallelogram divides it into two congruent triangles.

### What theorem proves a quadrilateral is a parallelogram?

Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent. 2. Now, let’s prove that if a quadrilateral has opposite sides congruent, then its diagonals divide the quadrilateral into congruent triangles….Theorems about Quadrilaterals.

Statements Reasons
Parallelogram \begin{align*}ABCD\end{align*} Given

How do you read a quadrilateral Class 9?

A plane figure bounded by four sides is called a quadrilateral.

1. • Sum of the angles of a quadrilateral is 360°.
2. • A quadrilateral is a parallelogram, if.
3. • A diagonal of a parallelogram divides it into two congruent triangles.
4. • Diagonals of a rhombus bisect each other at right angles, and vice versa.

What are the types of Quadrilaterals Class 9?

There are mainly 6 types of quadrilaterals which are:

• Trapezium.
• Parallelogram.
• Rectangle.
• Rhombus.
• Square.
• Kite.

## How do you prove a quadrilateral is a rhombus Class 9?

If the diagonals of a quadrilateral bisect all the angles, then it’s a rhombus (converse of a property). If the diagonals of a quadrilateral are perpendicular bisectors of each other, then it’s a rhombus (converse of a property).

### Why ABCD is a parallelogram?

The shape of quadrilateral ABCD changes as the moving platform swings around, but its side lengths do not change. Both pairs of opposite sides are congruent, so ABCD is a parallelogram by the Parallelogram Opposite Sides Converse. By the definition of a parallelogram, — AB — DC .

What is quadrilateral for 9th standard?

A figure formed by joining four non-collinear points is called a quadrilateral. In other words, it is a four-sided polygon. It has four sides and four vertices. By joining the opposite vertices of the quadrilateral, we obtain a diagonal.

Which is the best quadrilateral for CBSE Class 9?

Question.24 ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. Prove that : [CBSE-15-6DWMW5A] Solution. Question.25 In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. [CBSE March 2012] Solution.

## What are the theorems of quadrilaterals in maths?

Theorem 3: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. ( Proof) Theorem 4: In a parallelogram, opposite angles are equal. ( See Proof) Theorem 5: If each pair of opposite angles of a quadrilateral is equal, then it is a parallelogram.

### Which is the best question for quadrilateral PQRS?

Question.7 In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:3:7, then find the measure of∠S. Solution. Question.8 If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram. Solution.

What are quadrilaterals for Class 9 Maths Chapter 8?

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals are an educational aid for students that help them solve and learn simple and difficult tasks. It includes complete set of questions organized with advanced level of difficulty, which provide students ample opportunity to apply combination and skills. 