# Solution - Similarity of Triangles

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ConceptSimilarity of Triangles

#### Question

Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

#### Solution

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See the given Figure.  DE || BC. Find EC

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In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

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Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

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Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

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In the following figure, DE || OQ and DF || OR, show that EF || QR

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Solution for concept: Similarity of Triangles. For the course 9th - 10th SSC (English Medium)
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