Two parallelogram stand on equal bases and between the same parallel the ratio of their areas is

Two parallelograms stand on equal bases and between the same parallels.

Question:

Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is
(a) 1 : 2
(b) 2 : 1
(c) 1 : 3
(d) 1 : 1

Solution:

(d) 1:1

Area of a parallelogram = base ⨯ height

Answer (Detailed Solution Below)

Option 1 : 1 : 1

Free

15 Qs. 15 Marks 12 Mins

Given:

Two parallelograms stand on equal bases and between the same parallel.

Theorem Used: 

Parallelograms on the same base and between the same parallels are equal in area.

Calculation:

Consider the figure presented above. Now ΔBCE and ΔADF will be congruent. Let us prove this. We have:

1.  BC = AD (opposite sides of a parallelogram are equal)
2.  ∠BCE = ∠ADF (corresponding angles)
3.  ∠BEC = ∠AFD (corresponding angles)

By the ASA criterion, the two triangles are congruent, which means that their areas are equal.

∴ Hence Proved.

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Text Solution

`1 : 2``1 : 1``2 : 1``3 : 1`

Answer : B

Solution : We know that, parallelogram on the equal bases and between the same parallels are equal in area. So, ratio of their areas is `1 : 1`.

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Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is a 1 : 2 b 2 : 1 c 1 : 3 d 1 : 1