# RD Sharma Class 9 Chapter 14 Solutions (Quadrilaterals)

RD Sharma Maths solutions for class 9 chapter 14 Quadrilaterals will review all your concepts learned in this chapter on quadrilaterals. So here we have our suite of Instasolv RD Sharma Solutions grade 9 maths solutions to help you in your quest to better understand quadrilaterals.

This chapter has 32 questions and 5 exercises that are properly solved in simple methods. As we all know that any shape with four sides is said to be quadrilaterals. In this chapter, we will focus on the different types of quadrilaterals with proofs such as square, rectangle, and parallelogram properties. This chapter also focuses on two other terms which are very important from the exam point of view. They are simple and complex quadrilaterals. In this chapter, you will find a blend of both types of questions. Sometimes you will need to solve numerically and sometimes you would need to prove according to the questions.

The most important intention of RD Sharma maths solution for class 9 is to assist you to self analyze the areas which require extra exercise from the examination factor of view. With the help of Instasolv RD Sharma Solutions, you can solve the exercise problems in less time with a clear idea of concepts.

## Important topics for RD Sharma solutions for class 9 chapter 14 Quadrilaterals

- Quadrilaterals are classified based on their intersecting nature. If they do not intersect, they are called simple quadrilaterals. Otherwise, if they accidentally intersect, this is known as a complex quadrilateral.
- The chapter introduces you to a new concept: A
**parallelogram**is a quadrilateral with opposite sides parallel (hence the angles on the other side are equal). - Squares with the same sides are called
**rhombuses**, and parallelograms with all right angles are called rectangles. - In this chapter, you will learn about some important concepts of the parallelogram.
- The first concept of Parallelogram: Opposite sides of a parallelogram are equal

- A parallelogram is a simple quadrilateral with two pairs of parallel sides. The sides opposite or parallel to the quadrilateral have equal lengths and the angles opposite the parallelogram have the same length.
- The second concept of parallelogram: The Opposite angles in a parallelogram are equal.

The angles against the parallelogram are the same (and vice versa: if the angle against the quadrilateral is the same, it is the parallelogram). The quadrilateral diagonals of each other (and vice versa: if the quadrilateral diagonal divides one another, it is a parallelogram).

- The next important topic of this chapter will be the Properties of diagonal of a parallelogram.

**Diagonals of a parallelogram bisect each other.**

In any parallelogram, the diagonals (lines connecting the opposite corners) separate from each other. That is each diagonal cuts the other into two equal parts. In the figure above, drag any vertex to change the parallelogram and convince yourself that it is.

- If the diagonal of quadrilaterals is divided among itself, it is a parallelogram.
- The diagonal of the parallelogram divides it into two congruent triangles.

- In chapter 14 quadrilaterals you will also focus on the Diagonals of a rhombus that bisect each other at right angles( 90 degrees)

- You will also get to know that the Diagonals of a rectangle bisect each other and are equal.

- At the same time, you will also get to know that the Diagonals of a square bisect each other at right angles and are equal.

- Next, we will also discuss some of the Important results concerning parallelogram.

**ABCD parallelogram**

- Sides opposite to parallelograms are always parallel and equal.

AB||CD, AD||BC, AB=CD,AD=BC

- Angles opposite to a parallelogram are always said to be equal to adjacent angles that are supplementary.

∠A=∠C,∠B=∠D,

∠A+∠B=1800, ∠B+∠C=1800, ∠C+∠D=1800, ∠D+∠A=1800

- Parallelogram diagonals divide it into 2
**congruent triangles**.

ΔABC≅ΔCDA [Concerning AC as diagonal]

ΔADB≅ΔCBD [Concerning BD as diagonal]

- The parallelogram diagonals always bisect each other.

**Another vital topic of this chapter quadrilateral will be “The Mid-Point Theorem”.**

The line segment connecting the midpoints on both sides of the triangle is parallel to the third side and is half of the third side.

- Simple quadrilaterals are further classified into concave and convex quadrilaterals based on their diagonal position and their interior angles. This chapter will also give you an idea about polygons with 4 verticals.

**Exercise discussion for RD Sharma solutions for class 9 chapter 14 Quadrilaterals**

- As mentioned above, in this chapter there are five exercises.
- The first set of questions in exercise 14 A has 4 questions.
- In this exercise, you will learn about different quadrilateral angles, their properties, and more. With a strong foundation in all major mathematical topics, you are ready to solve the most difficult problems of algebraic problems based on Quadrilaterals’ consecutive or adjacent sides, opposite sides of a Quadrilateral, Quadrilaterals consecutive angles, Quadrilaterals opposite angles and the angle sum property of Quadrilaterals.
- The second set of questions in exercise 14.2 that has 4 questions that will ask you to solve problems related to Various Types of Quadrilaterals (Trapezium, Isosceles Trapezium, Parallelogram, Rhombus, Rectangle, and Square). In this exercise, you will get an idea about different Properties of parallelograms and Some important theorems on Quadrilaterals.
- The third set of questions in exercise 14.3 has 4 questions. This exercise will increase your knowledge of different concepts and conditions that are vital for quadrilaterals to be a parallelogram and some important theorems results.
- The fourth set from exercise 14.4 has 10 questions which are based on useful facts about the triangle. This exercise will ask you to discuss some results on the theorems of triangles.
- The last set of 10 questions will be from an exercise named Very short answer type solution. This section allows you to revise the whole chapter of quadrilaterals. This section is a mixture of important topics that include different types of quadrilaterals, special cases, and many more.

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