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Class 9 Math Ratio and Proportion


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3.Showthatinanycorrespondenceoftwotrianglesiftwoanglesofonetrianglearecongruenttothecorrespondinganglesoftheotherthenthetrianglesaresimilar.3. Show that in any correspondence of two triangles if two angles of one triangle are congruent to the corresponding angles of the other then the triangles are similar.

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.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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