Similarity and geometry shape
Similarity: Two objects are similar if the angles one object is equal to the angles of the other and if the sides of one object are in proportion with the sides of the other. It is important to remember that the shape of both the object however remains the same.
The general form of a quadratic equation is ax2+ bx+ c=y, where a = 0 and a,b,c are the parameters which influence its U-shaped parabola graph. This is an example of a non-linear function with its highest exponent 2.
Probability is the study of the chances a particular event has, as any event happening has certain outcomes. So the measure of probability ranges from ‘0’ (event not happening-0%chance) to ‘1’ (event happening for sure-100%chance).
The 6 trigonometric functions when graphed in an x-y coordinate plane, give different measurements based on their side and angle. The sign of the trigonometric functions depends on how the angle is formed.
Square root functions (for example: y= √x) is defined as the function where the output ‘y’ when multiplied by itself (squared) gives the input ‘x’. The symbol ‘√’is called the ‘radical symbol’ and the general form of any square root function is given by:
Trigonometry can be used in finding the measure of the angles, their function values and also the sides of a triangle. The 6 trigonometric functions can be used to find the remaining side or angle in a right triangle. These calculations give rise to trigonometric ratios in a right triangle.
Congruence geometry: If two objects are of same exact shape and same exact size, then they are called congruent objects. The congruent objects are more like duplicates of each other and fit perfectly when placed on top of each other.
In geometry, congruency is an important property and whenever two geometric shapes have same shape and length, then the angles of one shape are also equal to the other.
Example:
The symbol used to denote congruency is, ‘≡’ which means that the structures are of same shape and equal size.
Congruency in triangles:
Theorems:
SSS: 3 sides of one triangle=3 sides of the other
2) SAS :2 sides and included angle of one triangle=2 sides and included angle of other.
3)ASA :2 angles and included side one triangle= 2 angles and included side of other.
4) AAS :2angles and non-included side=2angles and non-included side of other
Example: If ∆ ABC≡∆DEF and BC=10 units, then EF=? EF=10 (since BC=EF )
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| You can also Read our other blog Angle Definition And Properties (Trigonometry) |
Angle Definition : Angle is the measure of rotation formed between two rays. In trigonometry, angles play a huge role in determining the appropriate trigonometric function values. One complete rotation gives an angle of 360°. Depending on the direction of rotation, angles can be positive or negative!
Units of Angle: Angle is either measured in degrees or in radians.
Radian: It is the standard unit to measure an angle and is numerically equal to the length of its respective arc of a unit circle.
Conversion of degree to radian: There is a simple relationship between degrees and radians.
Π radians = 180°
So 1radian=180°/Π (OR) 1degree=π/180°
Example: Convert 120° to radian.
120°* (π /180°) = 2π/3 radian
Example: Convert π/6 radian to degrees.
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| You can also Read our other blog Intro To Inverse Trigonometric Functions |
In trigonometry, if an angle is given then using any of the 6 trigonometric functions we find its trigonometric function value. But if the trigonometric function value is given, then finding the angle (working backwards) using a function is called Inverse trigonometric function.