Question

13. ABC is an equilateral triangle, AD and
BE are perpendiculars to BC and AC
respectively. Prove that :
(i) AD = BE
(ii) BD = CE​

Answer 1

Given

∆ABC is a equilateral triangle

AD ⊥BC

BE ⊥AC

To Prove

(i) AD = BE

(ii) BD = CE

Prove

Consider ∆ ADC & ∆ BEC

• BC=AC [side of equilateral triangle is equal]

• ∠BC= ACB [ common]

• ∠ADC= AEC [ 90° angle ]

Therefore ∆ADC =∆ BEC by AAS criteria.

By CPCT(Corresponding parts of congruent Triangle)

• AD= BE
• BD= CE

Hence proved

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