Mathematics

# On the sides, AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn. Prove that:  $\angle {\text{CAD}} = \angle {\text{BAE}}$

##### SOLUTION
Given:$\triangle{ABD}$ and $\triangle{ACE}$ are equilateral triangle.

$\therefore$ In $\triangle{ABD}$

$\angle{BAD}=\angle{ABD}=\angle{BDA}={60}^{\circ}$  .....$(1)$

In $\triangle{ACE}$

$\angle{AEC}=\angle{ACE}=\angle{ACE}={60}^{\circ}$  .....$(2)$

To prove:$\angle{CAD}=\angle{BAE}$

Proof:$\angle{CAD}=\angle{BAC}+\angle{DAB}$

$\Rightarrow \angle{CAD}=\angle{BAC}+{60}^{\circ}$ using $(1)$

$\Rightarrow \angle{CAD}=\angle{BAC}+\angle{CAE}$ using $(2)$

$\Rightarrow \angle{CAD}=\angle{BAE}$

Hence proved.

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Subjective Medium Published on 09th 09, 2020
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