PROVING SIMILARITY

Proving similarity - Description

Similar Figures – GCSE Maths (Edexcel & AQA)

What are Similar Figures?

Two shapes are said to be similar if:

Their corresponding angles are equal

Their corresponding sides are in the same ratio

This means the shapes look the same (same shape) but may be different sizes.

Conditions for Similarity

1. For Triangles:

AA (Angle-Angle): Two angles of one triangle equal two angles of another.

SSS (Side-Side-Side) in proportion: All three sides are in the same ratio.

SAS (Side-Angle-Side) in proportion: Two sides in the same ratio and the angle between them is equal.

2. For Other Shapes:

All corresponding angles must be equal

All corresponding sides must be in the same ratio

Scale Factors in Similar Figures

1. Length Scale Factor (LSF):

LSF=length of one side/length of corresponding side

Used to compare linear dimensions (length, width, height)

2. Area Scale Factor (ASF):

ASF= (LSF)^2

Area increases by the square of the length scale factor.

ASF=area of figure 1/area of figure 2

3. Volume Scale Factor (VSF):

VSF = (LSF)^3

Volume increases by the cube of the length scale factor.

Volume scale factor=volume of figure 1/volume of figure 2

Application in 2D and 3D Figures

In 2D Shapes (like triangles, rectangles, etc.):

Identify the LSF

Use it to find missing sides or areas

Check if angles are equal to confirm similarity