GEOMETRY TERMS AND DEFINITIONS WITH PICTURES

Definition : 

Certain statements are being made in order to create new concepts from the existing without leading to wrong results. Such of the statements are called definitions.

Examples :

1) A triangle is called equilateral if all the sides are of the same length.

2) Two angles are called supplementary if their sum is 180°.

Axiom :

There are certain statements which are assumed to be true. These statements are called axioms.

Examples :

1) There is exactly one and only one straight line passing through two given points.

2) If n is a natural number, then n+1 is also is also a natural number.

Symbol : 

A symbol is nothing but a particular mark which refers to some information.

Some of the symbols and the information indicated by them are given below.

Axiom :

There are certain statements which are assumed to be true. These statements are called axioms.

Examples :

1) There is exactly one and only one straight line passing through two given points.

2) If n is a natural number, then n+1 is also is also a natural number.

Congruence ≅ :

Congruent means equal in all respects or figures whose shapes and sizes are both the same. Now let us discuss about congruent of triangle. 

If the sides and angles of one triangle are equal to the corresponding sides and angles of each other triangle.

In the above pictures the first and third triangles are congruent to each other. So we can say triangle 1 and triangle 3 are congruent.

Conjecture :

A statement until it is proved or disproved called a conjecture.

Now we are going to see as how a theorem is defined on Geometry dictionary

Theorem :

A conjecture if it is proved becomes a theorem. Thus a statement which has been proved to be true is called theorems. A conjecture, if it is not proven becomes a false statement.

here we can see about points on Geometry dictionary

Point :

A point is used to represent a position in space. In practice, we put a small dot on paper or on a blackboard to indicate a point. But theoretically a point that does not has shape or size. The following Letters A,B,C, and D re the examples of point

Now we are going to see about lines in Geometry Dictionary

Line :

A set of points that extend infinitely in opposite directions is called a line. We use the symbol. The line has many points.

Line segment :

The line segment is a part of the line which is having two end points

Collinear points :

If three or more points are on a same line, then the points are called collinear points.

Ray :

Ray is nothing but a part of a line with one end point.

Now we are going to look at Angles on Geometry Dictionary

Angle :

The angle is formed by two rays with common end points, called vertex

Angle bisector :

The angle bisector of an angle is the line, which separates the angle. The bisector is nothing but dividing the angle as two equal parts.

Here OX is the angle bisector of angle BOA Hence angle AOX = angle BOX

Angle bisector of a triangle :

The angle bisector of any triangle is the line segment which bisects an angle of a triangle Here AD is the angle bisector of triangle ABC.anglebisector.GIF

Planes :

Planes are special sets of points. It is a flat surface that extends indefinitely in all directions.

Intersecting of lines :

Intersecting lines are lines that lie in the same plane and meet in a point.

In the above diagram there are two lines intersecting at the point A. This point is called intersection point or point of intersection

Two kinds of angles can be formed when two lines are intersecting.

1) Vertical angle

2) Adjacent angle

Circle :

The collection of all the points in the plane, which are which are at a fixed distance from a fixed point in the plane, is called a circle.

Center :

The fixed point is called the center of that particular circle and the fixed distance is called the radius of the circle.

Diameter :

Take any two points on the circle. Here we have taken P and Q The length of PQ is called the diameter of the circle. Diameter divides the circle into two parts (semi circle) Diameter always passing through the center.

Chord :

The line joining any two points on the circumference of a circle is called chord of the circle. It does not pass through the center. Here PQ is called the diameter of the circle and AB is called a chord.

Arc :

A piece of a circle between two points is called an Arc. It can be classified into two parts

1)  Major arc
2)  Minor arc

Two circles intersecting in one point :

Two circles are said to touch each other if they should meet at a point and can have a common tangent at this point.

Circles touching externally :

When two circles touch each other, either they will touch each other internally or externally.

We can say two circles touch each other externally when they lie on the opposite sides of the common tangent.

Incenter of a circle :

The point of intersection of the angles of a triangle is called in-center. It is denoted by the letter “I”

Altitude of a Triangle :

The line segment of the perpendicular from a vertex to the opposite side of a triangle is called its altitude.

In the above triangle ABC the line AD is perpendicular to the line BC and it produces 90 degrees. So the line AD is called altitude of triangle.

Orthocenter of a triangle :

The point of concurrence of the altitudes from the vertices to the opposite sides of a triangle is called the orthocenter of the triangle.

The points of concurrence of all the three altitudes of a triangle are called the orthocenter of the triangle.

Median of a triangle :

A median of the triangle is the line segment that joins a vertex to the midpoint of the opposite side

Here AD is the median of the triangle.

Centroid of the triangle :

The point of the concurrence of the medians of a triangle is called centroid of the triangle.

Here the point G is called centroid of the triangle.

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You can also visit the following web pages on different stuff in math. 

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

COORDINATE GEOMETRY

Coordinate geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Coordinate geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

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