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Class 9Class 10First YearSecond Year
$3. In \Delta \mathrm{LMN} shown in the figure \overline{\mathrm{MN}} \| \overline{\mathrm{PQ}} (i) If \mathrm{mLM}=5 \mathrm{~cm} \mathrm{mLP}=2.5 \mathrm{~cm} \mathrm{mLQ}=2.3 \mathrm{~cm} then find \mathrm{mLN} .(ii) If \mathrm{mLM}=6 \mathrm{~cm} \mathrm{mLQ}=2.5 \mathrm{~cm} \mathrm{~m} \overline{\mathrm{QN}}=5 \mathrm{~cm}$

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

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

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

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

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

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