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Answer 1

Question:-

△ABC is an equilateral triangle. C is the mid-point of DE. ∠DAC and ∠EBC are equal and supplementary. Prove that △DAC ≅ △EBC

Answer:-

Given:

• △ABC is equilateral. That means AC = BC = AB
• C is mid-point of DE. That means DC = CE
• ∠DAC = ∠EBC and they are supplementary.

To prove:

△DAC ≅ △EBC

Proof:

In △DAC ≅ △EBC,

• AC = BC (As it is given that △ABC is equilateral)
• ∠DAC = ∠EBC (Given)
• DC = CE (As it is given that C is mid-point of DE)

∴ △DAC ≅ △EBC (SAS congruency)

Hence proved.