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? |
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 |
For more visit Constructing SSS Congruent Triangles – Rules and Solved Questions
