Related InterviewSolutions

• In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that ``
• If each diagonal of a quadrilateral separates itinto two triangles of equal area then show that the quadrilateral is aparallelogram.GIVEN : A quadrilateral `A B C D`such that its diagonals `A C`and `B D`are such that `a r( A B D)=a r( C D B`) and `a r( A B C)=a r( A C D)dot`TO PROVE: Quadrilateral `A B C D`is a parallelogram.
• In the figure, ABCD is a quadrilateral. A line DP drawn parallel to diagonal AC from point D, meet BC produced at P. Prove that: are of `Delta ABP = " area of " square ABCD`
• In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB respectively of `Delta ABC`. Prove that: (i) `square BDEF` is a parallelogram (ii) area of `Delta DEF = (1)/(4) xx " area of " Delta ABC` (iii) area of `square BDEF = (1)/(2) xx " area of " Delta ABC`
• `A B C D`is a parallelogram `X`and `Y`are the mid-points of `B C`and `C D`respectively. Prove that `a r( A X Y)=3/8a r(^(gm)A B C D)`GIVEN : A parallelogram `A B C D`in which `X`and `Y`are the mid-points of `B C`and `C D`respectively.TO PROVE : `a r( A X Y)=3/8a r(^(gm)a b c d)`CONSTRUCTION : Join `B Ddot`
• In figure, `CD || AE` and `CY || BA`. Prove that `ar (DeltaCBX) = ar (DeltaAXY)`.
• Parallelogram `A B C D`and rectangle `A B E F`have the same base `A B`and also have equal areas. Show that the perimeter ofthe parallelogram is greater than that of the rectangle.GIVE : `A ^(gm)A B C D`and a rectangle `A B E F`with the same base `A B`and equal areas.TO PROVE : Perimeter of `^(gm)A B C D > P e r i m e t e rofr e c t a nge l`ABEFi.e. `A B+B C+C D+A D > A B+B E+E F+A F`
• In a parallelogram `A B C D ,E ,F`are any two points on the sides `A B`and `B C`respectively. Show that `a r( A D F)=a r( D C E)dot`
• If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is equal to half of the parallelogram. GIVEN : `A ABC and ||^(gm)BCDE` on the same base BC and between the same parallels `BC and AD`. TO PROVE : `ar(ABC=1/2 ar(||^(gm)BCDE)` CONSTRUCTION : Draw `AL _|_ BC and DM _|_ bc`, metting BC produced in M.
• The area of a parallelogram is `150cm^(2)`. If the ratio of its base and corresponding altitude is `3 : 2`, find the length of base and altitude