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In the figure, arms $BA$ and $BC$ of $\angle ABC$ are respectively parallel to arms $ED$ and $EF$ of $\angle DEF$. Prove that $\angle ABC = \angle DEF$."

Academic Mathematics NCERT Class 9

Given:

In the figure, arms $BA$ and $BC$ of $\angle ABC$ are respectively parallel to arms $ED$ and $EF$ of $\angle DEF$.

To do:

We have to prove that $\angle ABC = \angle DEF$.

Solution:

Produce $BC$ to meet $DE$ at $G$

$AB \parallel DE$

This implies,

$\angle ABC = \angle DGH$.........…(i) (Corresponding angles)

$BH \parallel EF$

$\angle DGH = \angle DEF$................(ii) (Corresponding angles)

From (i) and (ii), we get,

$\angle ABC = \angle DEF$.

Hence proved.

Updated on: 10-Oct-2022

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