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

lwfrgin

lwfrgin

Answered question

2021-08-09

Write a proof for the following:
Given AB=DE and C is the midpoint of both AB and BE.
Prove: ABC=DEC.

Answer & Explanation

curwyrm

curwyrm

Skilled2021-08-10Added 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)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?