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#### Question

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

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

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.

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).

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).

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