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.