Question

which criterion of similarity will be used in proving that ∆ABD=∆ACE?​

Answer 1

Answer:

See this attachment...

Answer 2

Complete Question :- In the figure, point D and E are on side BC of ∆ABC, such that BD = CE and AD = AE . which criterion of similarity will be used in proving that ∆ABD ≅ ∆ACE ?

Answer :-

In ∆ADE we have,

→ AD = AE (given)

so,

→ ∠ADE = ∠AED (Angles opposite to equal sides are equal.) --------- Eqn.(1)

Now,

→ ∠ADE + ∠ADB = 180° (Linear pair angles.) ----- Eqn.(2)

→ ∠AED + ∠AEC = 180° (Linear pair angles.) ------ Eqn.(3)

putting Value of Eqn.(1) and subtracting Eqn.(3) from Eqn.(2),

→ ∠ADB − ∠AEC = 0

→ ∠ADB = ∠AEC --------- Eqn.(4)

now, in ∆ABD and ∆ACE , we have,

→ ∠ADB = ∠AEC {Eqn.(4)}

→ BD = CE (Given)

→ AD = AE (Given)

therefore,

→ ∆ABD ≅ ∆ACE (By SAS congruency.)

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