Prove that Parallelograms on the same base and between the
same parallels are equal in area.
Text Solution
Verified by Experts
Since opposite sides of parallelogram are equal,
`AD||BC` with transversal `AB`
`/_DAB=/_CBF` (Corresponding angles)
And, `AD=BC` (opposite sides of parallelogram are equal)
In `/_\AED` and `/_\BFC`
`/_DEA=/_CFE`
`/_DAB=/_CBF`
...
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 9.2|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 9.3|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.10|1 Videos
LINES AND ANGLES
NCERT ENGLISH|Exercise Exercise 6.1|6 Videos
NUMBER SYSTEMS
NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
Similar Questions
Explore conceptually related problems
Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.
Prove by vector method that the parallelogram on the same base and between the same parallels are equal in area.
Triangles on the same base and between the same parallels are equal in area.
If a triangle and a parallelogram are on the same base and between the same parallels lines, then the area of the triangle is equal to half that of the parallelogram. GIVEN : A triangle ABC and ||^(gm)BCDE on the same base BC and between the same parallels BC and AD . TO PROVE : ar (triangle ABC) =1/2 ar (||^(gm)BCDE) CONSTRUCTION : Draw AL _|_ BC and DM _|_ BC, produced at M.
A triangle and a parallelogram are on the same base and between the same parallels. The ratio of the areas of triangle and parallelogram is (a)1:1 (b) 1:2 (c) 2:1 (d) 1:3
If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.
If a triangle and a parallelogram are on the same base and between same parallels, then the ratio of the area of the triangle to the area of parallelogram is
Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is
Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is
Prove that two triangles having the same base and equal areas lie between the same parallels.