Example: Any two line segments are similar since length are proportional Any two circles are similar since radii are proportional Any two squares are similar since corresponding angles are equal and lengths are proportional. Note: Similar figures are congruent if there is one to one correspondence between the figures. Any two triangles are similar, if their. Statement: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Theorem 2. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Note: If the areas of two similar triangles are equal, the triangles are congruent. Statement: Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Statement: Prove that, in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
All congruent figures are similar but all similar figures are not congruent. SIMILAR POLYGONS Two polygons are said to be similar to each other, if: i their corresponding angles are equal, and ii the lengths of their corresponding sides are proportional Example: Any two line segments are similar since length are proportional Any two circles are similar since radii are proportional Any two squares are similar since corresponding angles are equal and lengths are proportional.
If two triangles are equiangular, then they are similar. Corollary AA similarity. If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
SSS Similarity Criterion. If the corresponding sides of two triangles are proportional, then they are similar. SAS Similarity Criterion. If in two triangles, one pair of corresponding sides are proportional and the included angles are equal, then the two triangles are similar. BD ii Result on Acute Triangles. RD Sharma Class 12 Solutions. Watch Youtube Videos.
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