## How do you prove a quadrilateral is 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. Hence, proved.

## How do you prove a quadrilateral theorem?

Draw a quadrilateral with diagonals that bisect each other and preview the proof. Your goal will be to show that there are two pairs of congruent triangles created by these diagonals. Then, you can show that alternate interior angles are congruent and therefore the opposite sides must be parallel.

**What are theorems in math class 9?**

Theorem: The sides opposite to equal angles of a triangle are equal. Theorem: If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). Theorem: In any triangle, the side opposite to the larger (greater) angle is longer.

**How many theorems are there in class 9 quadrilateral?**

1st Theorem- The diagonal divides the parallelogram into two congruent triangles. 2nd Theorem- The opposite side of a parallelogram are equal. 3rd Theorem- The quadrilaterals in which each pair of opposite sides are equal are called parallelogram. 4th Theorem- The opposite angles of a parallelogram are equal.

### How many theorems are there in quadrilateral Class 9?

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

The only shape you can make is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

**How do you prove a quadrilateral is a rectangle?**

There are a few ways to prove a quadrilateral is a rectangle. Here are three of the easiest ways: 1) Show all angles are 90°; 2) Show that one pair of sides is parallel and that two opposite angles are 90°; 3) Show the diagonals bisect each other and are of equal length.

**How many theorems are there in Quadrilaterals Class 9?**

#### What is a quadrilateral According to NCERT solutions for Class 9 Maths?

These solutions are explained by subject matter experts to help you in clearing all the doubts. What is the meaning of quadrilaterals according to NCERT Solutions for Class 9 Maths Chapter 8? According to NCERT Solutions for Class 9 Maths Chapter 8 quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

#### What is the converse of the quadrilateral theorem?

Thus, Theorem 8.2 can be stated as given below : If a quadrilateral is a parallelogram, then each pair of its opposite sides is equal. So its converse is : Theorem 8.3 : If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

**What is NCERT for Class 9 Maths Chapter 8?**

It includes a complete set of questions organized with advanced level of difficulty, which provide students ample opportunity to apply combinations and skills. Get free NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals devised according to the latest update on term-wise CBSE Syllabus for 2021-22.

**What is Theorem 8 of the quadrilateral theorem?**

Theorem 8. 8 A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. Given: ABCD is a quadrilateral where AB CD & AB = CD To Prove: ABCD is a Parallelogram Proof: Given AB CD with transversal AC.