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similar objects To know the idea of similarity and the ability to recognize similar objects To know about the meaning and the definition of the term similarity. To understand what are similar triangles. To know the different properties of similar triangles and it’s condition to become similar triangles. similar objects Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. one can be obtained from the other by uniformly scaling (enlarging or shrinking), possibly with additional translation, rotation and reflection. For example, all circles are similar to each other, Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor 100º are similar if and only if 30º 50º corresponding are congruent angles and the lengths of corresponding sides are proportional. 100º 50º 30º Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are similar. Various groups of three will do. Triangles are similar if the measure of all three interior angles in one triangle are the same as the corresponding angles in the other. Since all three corresponding angles are equal, we can be sure the triangles are similar. Because the triangles are similar, this means that the three pairs of corresponding sides are in the same proportion to each other. But don't forget Similar triangles can be rotated and/or mirror images of each other (reflected). In the figure on the right, the two triangles have all three corresponding sides equal in length and so are still similar, even though one is the mirror image of the other and rotated. Triangles are similar if all three sides in one triangle are in the same proportion to the corresponding sides in the other. Since all three corresponding sides are the same length, we can be sure the triangles are similar. Because the triangles are similar, this means that the three angles at P,Q and R are equal to the angles L,M and N respectively. But don't forget Similar triangles can be rotated and/or mirror images of each other (reflected). In the figure on the right, each angle in one triangle is equal to the corresponding angle in the other, and so are still similar even though triangle is the mirror image of the other, rotated and bigger. Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal. The three angles and Since two corresponding pairs of sides are in the same proportion, and the included angles are equal, we can be sure the triangles are similar. But don't forget Similar triangles can be rotated and/or mirror images of each other (reflected). In the figure on the right, the two triangles are still similar, even though one is the mirror image of the other and rotated. 1.Identify the similar ones? 2.Check whether these triangles are similar?