In the diagram, if (AB) || (CE)  ,  AG = GD = DH = HB, then which of the following is correct?
I) ∆ACG ≅ ∆BEH
II) ∆CDE ≅ ∆DEB ≅ ∆DCA
III) ∆HFB ≅ ∆AFG

Correct option is B

​Given:
In the diagram, AB||CE, AG = GD = DH = HB
​Formula used:
If two lines are parallel, corresponding angles are equal.
Solution:
I. ΔACG≅ΔBEH
Since AB||CE and AG = GD = DH = HB, the corresponding angles are equal.
=> ΔACG≅ΔBEH
II. ΔCDE≅ΔDEB
Since AB||CEand AG = GD = DH = HB, the corresponding angles are equal.
=> ΔCDE≅ΔDEB
III. ΔHFB≅ΔAFG
Since AB||CE and AG = GD = DH = HB, the corresponding angles are equal.
But no relation is given about side AF, BF, or angles of the triangle HFB and AFG,
hence, this statement is not right.
​∴ The correct answer is option (4).​