1800-419-1234| Get a Call from us

# Triangle and Parallelogram of Same Base and Between the Same Parallels

## Summary

LearnNext Lesson Video

HD 3:51

The parallelograms are on the same base and between the same parallels.
Area of a Parallelogram = b × h
In both parallelograms:
•    The bases are equal.
•    The heights are equal.
Area of parallelogram ABCD = Area of parallelogram ABGH.
Parallelograms on the same base and between the same parallels are equal in area.
Theorem:
Prove that the area of the triangle is equal to half the area of the parallelogram, if they are on the same base and are between the same parallels.

Given:
Δ ABP and  parallelogram ABCD are on same base AB and between the same parallels AB and PC.
To Prove: ar (ΔABP) =1/2 ar ( ||gm ABCD)
Construction: Draw BQ || AP
Proof:
ar ( ||gm ABQP) = ar ( || gm ABCD (Parallelograms on the same base and between the same parallels are equal in area.)
Δ ABP ≅ Δ BQP
ar (Δ ABP) = ar (Δ BQP)
ar (Δ ABP) =  (½) ar (|| gm ABQP)
ar (Δ ABP) =  (½) ar (|| gm ABCD).

Recall that sum of angles of a polygon = (2n - 4) × 90°
Here number of sides, n = 9
Hence the sum of angles of the given pol...
Length = 21 cm