Question

a triangle ABC is an equilateral triangle C is the midpoint of DE. the angle DAC and angle EBC are equal and supplementary prove that triangle DAC congruent to triangle EBC

Answer 1

ABC is an equilateral Triangle,

AC=BC,

C is the midpoint of DE,

So DC=CE,

We have to prove that Triangle DAC and Triangle EBC both are congruent,

Now we join A and D, B and E,

In Triangle DAC and Triangle EBC,

1), DC = EC,

2)AC= BC,

3),Angle DAC = angle EBC= 90°, ( supplementary),

Therefore ,

triangle DAC congruent to triangle EBC, proved.