Q7 of 23 Page 22

In figure 2.27, if line AB || line CF and line BC || line ED then prove that ∠ ABC = ∠ FDE

Given: Line AB ∥ CF and line BC ∥ ED

To find: ∠ ABC = ∠ FDE


Construction: G and h in diagram.


AB ∥ CD and BC is transversal both


So, ∠ ABC = ∠ PCG (linear pair angle)



BC∥ ED and PF is transversal line to both


So, ∠ ECG = ∠ CDH


∠ CD = ∠ FDE (Both angle is opposite)


∴ ∠ ABC = ∠ FDE (hence proved)


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