In the given figure, AD//BC. If the areas of the triangle ABE and Triangle ACF are equal, then prove that EF//AC.
1 Answer
Given,
AD//BC and area of
Triangle ABE = area of triangle ACF
To prove: EF//AC
Construction: EC is joined.
Proof:
| S.N | Statements | Reasons |
| 1 | Triangle ABE = Triangle ACE | Being triangles on the same base and between the same parallel lines. |
| 2 | Triangle ABE = Triangle ACF | Given. |
| 3 | Triangle ACE = Triangle ACF | From statements (1) and (2), by equal quantity axiom. |
| 4 | ∴ EF//AC | From statement (3), being triangles on the same line segment and towards the same side of it equal in area. |
Verified.
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