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Congruent shapes in real life12/7/2023 ![]() ![]() Listed below are a few topics related to similar figures, take a look.įAQs on Similar Figures How is Similarity Used in Real Life? Consider the following figure, in which the sides of two triangles ΔABC and ΔDEF are respectively proportional: This essentially means that any such pair of triangles will be equiangular(All corresponding angle pairs are equal) also. The SSS similarity criterion states that if the three sides of one triangle are respectively proportional to the three sides of another, then the two triangles are similar. Using the AA criterion, we can say that these triangles are similar. Ideally, the name of this criterion should then be the AAA(Angle-Angle-Angle) criterion, but we call it as AA criterion because we need only two pairs of angles to be equal - the third pair will then automatically be equal by the angle sum property of triangles.Ĭonsider the following figure, in which ΔABC and ΔDEF are equi-angular,i.e., In short, equiangular triangles are similar. The AA criterion for triangle similarity states that if the three angles of one triangle are respectively equal to the three angles of the other, then the two triangles will be similar. Let us understand the similarity of triangles with the three theorems according to their angles and sides. All corresponding sides of triangles are proportional.All corresponding angle pairs of triangles are equal.Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides or scale factor must be the same. 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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