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Class 9 Math Ratio and Proportion


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Class 9Class 10First YearSecond Year
1.Whichofthefollowingaretrueandwhicharefalse?(i)Congruenttrianglesareofsamesizeandshape.(ii)Similartrianglesareofsameshapebutdifferentsizes.(iii)Symbolusedforcongruentis.(iv)Symbolusedforsimilarityis(v)Congruenttrianglesaresimilar.(vi).Similartrianglesarecongruent.(vii)Alinesegmenthasonlyonemidpoint.(viii)Oneandonlyonelinecanbedrawnthroughtwopoints.(ix)Proportionisnonequalityoftworatios.(x)Ratiohasnounit.1. Which of the following are true and which are false?(i) Congruent triangles are of same size and shape.(ii) Similar triangles are of same shape but different sizes.(iii) Symbol used for congruent is \cong.(iv) Symbol used for similarity is (v) Congruent triangles are similar.(vi). Similar triangles are congruent.(vii) A line segment has only one mid-point.(viii) One and only one line can be drawn through two points.(ix) Proportion is non-equality of two ratios.(x) Ratio has no unit.

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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