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##### 1. In \triangle \mathrm{ABC} as shown in the figure \overrightarrow{\mathrm{CD}} bisects \angle \mathrm{C} and meets \overline{\mathrm{AB}} at \mathrm{D} . \mathrm{mBD} is equal to \begin{array}{llll}\text { (a) } 5 & \text { (b) } 16 & \text { (c) } 10 & \text { (d) } 18 & \end{array}

1. In \triangle \mathrm{ABC} \overline{\mathrm{DE}} \| \overline{\mathrm{BC}} .(iv) If \mathrm{m} \overline{\mathrm{AD}}=2.4 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{AE}}=3.2 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{DE}}=2 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{BC}}=5 \mathrm{~cm} find \mathrm{m} \overline{\mathrm{AB}} \mathrm{m} \overline{\mathrm{DB}} \mathrm{m} \overline{\mathrm{AC}} \mathrm{m} \overline{\mathrm{CE}} .

2. In \triangle \mathrm{ABC} shown in the figure \overrightarrow{\mathrm{CD}} bisects \angle \mathrm{C} . If \mathrm{m} \overline{\mathrm{AC}}=3 \mathrm{~m} \overline{\mathrm{CB}}=6 and m \overline{A B}=7 then find m \overline{A D} and

4. Prove that the line segment drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side.

6. In Isosceles \triangle \mathrm{PQR} shown in the figure find the value of x and y .

4. In the shown figure let \mathrm{m} \overline{\mathrm{PA}}=8 x-7 \mathrm{~m} \overline{\mathrm{PB}}=4 x-3 \mathrm{m} \overline{\mathrm{AQ}}=5 x-3 \mathrm{~m} \overline{\mathrm{BR}}=3 x-1 . Find the value of x if \overline{\mathrm{AB}} \| \overline{\mathrm{QR}} .

5. Prove that the line segment joining the mid-points of any two sides of a triangle is parallel to the third side.