# Triangles and Quadrilaterals

This chapter is divided into several sections namely - congruence which explains the definition of congruence; congruence in triangles, SAS (side angle sides) and ASA (angle side angle) concepts and their proofs in various scenarios. Next, we have in depth explanation of triangles , distance from a point and line and angle bisectors including a series of examples to help better understand the concepts. Later, in this section we will walk through the definition of quadrilaterals and parallelogram, followed by various theorems involved, along with the theorem's proof and its properties to better the understand the structure of these polynomials.

In addition to preparing for the JEE mains and advanced exams, Cuemath Founder Manan Khurma's study material is helpful for students who are appearing for CBSE, ICSE and other State board exams.

## Congruence in Triangles

- What is Congruence
- Congruence in Triangles
- The SAS Criterion
- Is there an SSA Criterion?
- Perpendicular Bisectors
- The ASA Criterion
- The ASA Criterion Proof
- Is There an AAS Criterion?
- Isosceles Triangles
- The SSS Criterion
- The SSS Criterion - Proof
- The RHS Criterion
- The RHS Criterion - Proof

## More on Triangles

- Relative Magnitudes of Sides and Angles
- The Triangle Inequality
- Distance of a point from a line
- Angle Bisector

## Quadrilaterals and Parallelograms

- What is a Quadrilateral?
- Angle Sum Property in Quadrilaterals
- Some Particular Types of Quadrilaterals
- Parallelograms
- Properties of Parallelograms
- Mid-Point Theorem

## Areas of Parallelograms and Triangles

- Basic Area Concepts
- Same Base, Same Parallels
- Parallelograms - Same Base, Same Parallels
- Triangles - Same Base, Same Parallels
- Pythagoras Theorem

## Area of Triangles and Heron's Formula

## Basic Constructions

- Essence of Geometrical Constructions
- Constructing Angle Bisectors
- Constructing Perpendicular Bisectors
- Constructing an Angle of 90°
- Constructing an Angle of 60°
- Constructing Perpendicular from Point to Line

## Various Triangle Constructions

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