Triangles having the same base and between the same two parallels – Converse

# Triangles having the same base and between the same two parallels – Converse

In the previous segment, we proved that two triangles on the same base and between the two parallels have the same area. In this segment, we will learn if the converse of this is true.

 S.NO CONTENT 1 TRIANGLES ON SAME BASE AND BETWEEN SAME PARALLELS 2 SUMMARY 3 WHAT’S NEXT?

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## Triangles on the same base and between the same parallels – Converse

Consider two triangles: △XYZ and △PQR.

Base YZ = Base QR

Area (△XYZ) = Area (△PQR)

The height of △XYZ is XA and the height of △PQR is PB

Figure 1

 1 Area (△XYZ) = ½ x YZ x XA Area of triangle = ½ x base x height 2 Area (△PQR) = ½ x QR x PB Area of triangle = ½ x base x height 3 Area (△XYZ) = Area (△PQR) Given 4 ∴ ½ x YZ x XA = ½ x QR x PB ∴ YZ x XA = QR x PB From statements 1, 2, and 3

## Related content

 AREAS OF PARALLELOGRAMS AND TRIANGLESCongruent Figures Parallelograms on the Same Base and between the Same Parallel Lines – Part 1 Parallelograms on the Same Base and between the Same Parallel Lines – Part 2 A Triangle and a Parallelogram on the Same Base between the Same Parallel Lines Triangles Having The Same Base And Between The Same Two Parallel Lines

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