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Class 9 Math Ratio and Proportion


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1.InABCDEBC.(iv)IfmAD=2.4 cm mAE=3.2 cm mDE=2 cm mBC=5 cmfindmABmDBmACmCE.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}} .

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}} .
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}} .
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1.InABCDEBC.(iv)IfmAD=2.4 cm mAE=3.2 cm mDE=2 cm mBC=5 cmfindmABmDBmACmCE.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
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

2.InABCshowninthefigureCDbisectsC.IfmAC=3 mCB=6andmAB=7thenfindmADand2. 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.
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.

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

6.InIsoscelesPQRshowninthefigurefindthevalueofxandy.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}} .
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}} .

4.IntheshownfigureletmPA=8x7 mPB=4x3mAQ=5x3 mBR=3x1.FindthevalueofxifABQR.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.
5. Prove that the line segment joining the mid-points of any two sides of a triangle is parallel to the third side.

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

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