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Question

On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn.

Prove that: (i) CAD = BAE

(ii) CD = BE.

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Solution

Given: ABC is a triangle. ABD and ACE are equilateral

RTP: CD = BE

Construction: Join BE and CD.
Proof:
BAD= CAE [Angles of equilateral triangle]

BAD + BAD = CAE + BAC

[By adding BAC on both sides]


In ACD and ABE
AD = AB
AC = AE [equilateral triangle]


CAD= BAE {Proved}


ACD = AEB [According to SAS congruency]


Therefore CD = BE.


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