Write a proof for the following \overline{AB}\cong \overline{DE} and C is the midpoint of both \overline{AB}\ and\ \overline{BE}

lwfrgin 2021-08-09 Answered
Write a proof for the following:
Given AB=DE and C is the midpoint of both AB and BE.
Prove: ABC=DEC.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

curwyrm
Answered 2021-08-10 Author has 87 answers
Step 1
AB=DE and C is the mid point of both AD and BE.
Now
AC=DC...(1) ( C is mid point of AD)
CE=BC...(2) ( C is the mid point of BE)
ACB=BCE...(3) ( vertically opposite s)
Also AB=DE...(4) (Given)
Step 2
Therefore from (1), (2) and (4)
ABC=DEC (by SSS similarity)
Also from (1), (2) and (4)
ABC=DEC (by SAS similarity)
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more