Question

∆ABC is an equilateral triangle. C is the mid-point of DE. angle DAC
and angle EBC are equal and supplementary angles. Prove that
∆DAC
~
=
∆EBC.
​

Answer 1

Answer:

Your answer is here:-

Step-by-step explanation:

Given :- ∆ ABC is equilateral (AB = BC = AC) and DC= EC and < DAC = < EBC

In triangle DAC and EBC

AC = BC. ( given )

< DAC = < EBC ( given )

DC = EC ( given )

By SAS congruency rule

∆ DAC =~ ∆ EBC

Hope it helps you.

Answer 2

Answer:

Given:

• ∆ABC is an equilateral triangle. ( AC = BC )
• C is the mid-point of DE. ( DC = EC )
• angle DAC and angle EBC are equal and supplementary.

To Prove:

∆DAC is congruent to ∆EBC.

Proof:

In ∆DAC and ∆EBC,

• AC = BC ( given )
• angle DAC = angle EBC ( given )
• DC = EC ( given )

Hence, ∆DAC is congruent to ∆EBC by proving it using SAS congruency criterion.