Question 3: Explain the SAS similarity theorem?Īnswer: The SAS Similarity Theorem states that one triangle’s angle is congruent to another triangle’s corresponding angle such that the lengths of the sides, as well as these angles, are in proportion, then one can say that the triangles are similar. The corresponding sides of triangle are in the same ratio.Question 2: How can one find if the triangles are similar? If DE= 5 and MN=6, find A( △DEF)/A( △MNK)Īnswer : A( △DEF )/A ( △MNK )=DE²/MN² (areas of similar triangles) Question 1: It’s given that △ DEF ~ △ MNK.
Hence, we have proved that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, △ ABM ~ △ PQN …(AA test of similarity)Ī( △ A B C )/A ( △PQR )= …(from 1, 2 and 3)Ī( △ A B C )/A ( △PQR )= …(from 3) \( \angle AMB= \angle PNQ \) …(each side is a right angle) To Prove: A( △ A B C )/A ( △PQR ) =AB 2/PQ 2Ĭonstruction: Construct seg AM perpendicular side BC and seg PN perpendicular side QR The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides If two sides of two triangles are proportional and they have one corresponding angle congruent, the two triangles are said to be similar. If the corresponding sides of the two triangles are proportional the triangles must be similar. If two corresponding angles of the two triangles are congruent, the triangle must be similar. (C) Transitivity: If △ ABC ∼ △ DEF and △ DEF ∼ △ XYZ, then △ ABC ∼ △ XYZ Tests to prove that a triangle is similar (B) Symmetry: If △ ABC ∼ △ DEF, Then △ DEF ∼ △ ABC (A) Reflexivity: A triangle ( △) is similar to itself Basic Proportionality Theorem and Equal Intercept Theorem.Pythagoras Theorem and its Applications.The area, altitude, and volume of Similar triangles are in the same ratio as the ratio of the length of their sides. \( \angle ABC = \angle EGF, \angle BAC= \angle GEF, \angle EFG= \angle ACB \) The same shape of the triangle depends on the angle of the triangles. In the above diagram, we see that triangle EFG is an enlarged version of triangle ABC i.e., they have the same shape. Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.
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