Two triangles will be similar if the angles are equal ( corresponding angles) and sides are in the same ratio or proportion( corresponding sides). Hence, we can use the scale factor to get the dimensions of the changed figures. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively. For example, a rectangle has a length of 5 units and a width of 2 units.
This number helps in increasing or decreasing the figures in size but not in shape leaving them looking like similar figures. while dividing each set of corresponding side lengths, the number derived is the scale factor. Shapes are also considered to be similar when the ratios of the corresponding sides are equivalent i.e. "∼" but similar does not mean the same in size. The symbol to express similar figures is the same symbol for congruence i.e. For example, two circles (of any radii) are of the same shape but different sizes because they are similar. In geometry, when two shapes such as triangles, polygons, quadrilaterals, etc have the same dimension or common ratio but size or length is different, they are considered similar figures. When we magnify or demagnify these figures, they always superimpose each other. When two or more objects or figures appear the same or equal due to their shape, this property is known as a similarity or similar figures.
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