Introduction
Welcome Ninjas! This blog will go through a series of basic geometry knowledge, starting with the basics. We will begin the blog by introducing the classical concepts of straight lines, angles and triangles, followed by some sample questions.
Basic Geometry Concepts
Now we will start with our basic geometry knowledge:
Straight lines
Angles
A figure formed by two rays is called an angle.
 If angle AOB = 90 degrees, RIGHT ANGLE.
 If angle AOB < 90 degrees, ACUTE ANGLE.
 If angle AOB > 90 and AOB < 180 degrees, OBTUSE ANGLE.
 If angle AOB = 180 degrees, STRAIGHT ANGLE.
 If two angles add to form 90 degrees, they are called complementary angles.
 If two angles add to form 180 degrees, then it is called supplementary angles.
Triangle
 If AB=BC=AC, the triangle is an equilateral triangle.
 If AB=BC or AC=BC or AB=AC, the triangle is an isosceles triangle.
 If AB!=BC!=AC, the triangle is a scalene triangle.
Area of Triangle = ½ * base * height.
Here BC is the triangle’s base, and a line from A perpendicular to BC, AD will be the triangle’s height.
Therefore
Area of the triangle = ½ * a * h
Similar Triangles
We have two concepts when comparing two triangles; one of them is the ‘Similarity of triangles’.
We call two triangles to be similar if they have the same shape, but their size may or may not be the same. This means that the angles of the triangles are congruent (equal), and the sides of the triangles are proportional.
There are several ways to determine the two triangles to be similar:

AA Similarity
If two triangles have two congruent angles, they are similar. This is known as AA (angleangle) similarity.

SAS Similarity
When two triangles have two congruent sides, and the angle between them is congruent, they are similar. This is known as the SAS (sideangleside) similarity.

SSS Similarity
If two triangles have three congruent sides, they are similar. This is known as SSS (sidesideside) similarity.

HL Similarity
If the hypotenuse and one of the other sides of a rightangled triangle are congruent to the hypotenuse along with the corresponding side of the other right triangle, the two triangles are similar. This is known as HL (hypotenuseleg) similarity.
Congruent Triangles
Another concept we cover is of congruency of two triangles. We can say two triangles are congruent if one triangle can be made to superpose on the other to cover it exactly.
Below are some of the postulates for congruent triangles.

Side Angle Side (SAS) Congruence Postulate
If the two sides of one triangle and the angle between them are equal to the corresponding sides and angle of another triangle.

Angle Side Angle (ASA) Congruence Postulate
Two angles and the side between those angles of a triangle is equal to the relative two angles and the side between those two angles of another triangle.

Angle Angle Side (AAS) Congruence Postulate
Suppose any two angles and the nonincluded side of one triangle equal another triangle's corresponding angle and side. In that case, both triangles are said to be congruent.

Side Side Side (SSS) Congruence Postulate
All sides of a triangle are equal to the corresponding three sides of another triangle; then, both triangles are congruent.

Right Angle Hypotenuse (RHS) Congruence Postulate
If the hypotenuse and any of the sides of one right triangle are equal to the other triangle's same side and hypotenuse, then both triangles are congruent.
Some Theorems of Triangles
Some theorems which make our work easy while computing on triangles are listed below:

Carnot’s Theorem
Points D, E, and F are on the sides BC, AC and AB of a triangle named ABC. The perpendiculars corresponding to the sides of the triangle at points D, E and F are concurrent if and only if,
BD²DC²+CE²EA²+AF²FB² = 0

Ceva’s Theorem
If points D, E, and F are on the sides BC, CA and AB of triangle ABC, the lines AD, BE, and CF are concurrent at point P.
Then,
BD/DC * CE/EA * AF/FB = 1
Quadrilaterals
Let us know about some properties of quadrilaterals.
Properties  Rectangle  Square  Parallelogram  Rhombus  Trapezium 
All sides equal  ✗ 
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Opposite sides equal  ✓ 
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Parallel opposite sides  ✓ 
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All angles equal  ✓ 
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Equal opposite angles  ✓ 
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Sum of two adjacent angles equals a straight angle  ✓ 
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Diagonals bisect each other  ✓ 
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Diagonals bisect perpendicularly  ✗ 
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