Perimeter And Area Of Similar Figures

Perimeter is defined as the total of the peripheries of any figure that is the sum total of all sides of a figure. Perimeter is defined for almost every figure that is triangle, rectangle, square and others. For a Rectangle, a perimeter is determined by sum of all sides. Similarly perimeter of a triangle is determined by the sum of all sides of triangle. Area is termed as total area covered by any figure or  total space covered by any figure is defined as area for that figure. Perimeter and Area of Similar Figures may be equal or may not be equal as similarity is defined in different forms for Triangles. It includes SAS congruency, ASA congruency, RHS congruency, AAS congruency and SSS congruency. Any two triangles are said to be similar if they satisfy the above congruency conditions.

Here in above figure, triangle ABC is similar to triangle PQR by SAS congruency as two corresponding sides and angle between them are equal. Any two triangles are said to be similar by SAS stands for Side Angle Side congruency condition and if two sides corresponding to the triangles are equal and angle lying between them are also equal. If this congruency condition exists for triangles then those triangles will be similar to each other and it is represented by the symbol ‘~’. This symbol is substituted between two triangles and they are represented as similar.
ASA stands for Angle Side Angle congruency condition which explains that two triangles will be similar if two angles and one side between those angles will be equal. These angles must be corresponding to each other. Similarly, two triangles are said to be similar if both of them are right angled triangle that is one angle is 90⁰ and one side is equal in a corresponding manner. AAS stands for angle angle side congruency and according to this congruency condition, two triangles will be similar if two Adjacent Angles and one side are equal to two adjacent angles and one side of another triangle. SSS stands for Side Side Side congruency condition, as the name suggests two triangles are said to be similar by SSS when all three sides of one triangle are equal to all three sides of another triangle.