Similarity of Triangles by SSS criteria:
Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar. Given:
Construction: Cut PX = AB and PY = AC and join XY. Proof: It is given that Replacing AB with PX and AC with PY Subtract 1 from both sides [Converse of Basic Proportionality Theorem] Now XY || QR and PQ is the transversal Therefore [Corresponding Angles are equal] Now in [Common ] [Proved Above] [Proved Above] Therefore ..................(1) .....................(2) We know that AB = PX and AC= PY replacing AB and AC in Equation (2) .....................(3) From (1) and (3) BC= XY AB = PX [By Construction ] AC = PY [By Construction ] BC = XY [ Proved Above ] Therefore [By SSS Criterion] Hence |
Illustration : Find the value of E. Solution:
That is So Therefore
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The above two triangles are similar by _______________ criteria. | |||
Right Option : B | |||
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If the above triangles are similar, then write the similarity criteria. | |||
Right Option : B | |||
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Check whether the two triangles are similar or not. If so, then write the similarity criteria. | |||
Right Option : D | |||
View Explanation |
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