Write a paragraph proof to show that triangle ABC is congruent to triangle DEC
Given: line AC is congruent to line DC and line BC is congruent to line CE

Question

Write a paragraph proof to show that triangle ABC is congruent to triangle DEC
Given: line AC is congruent to line DC and line BC is congruent to line CE

anonymous · Answer

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anonymous · Answer

So I already know that 
Statement                                                                          Reason
1. Line AC is congruent to line DC and line BC is                  1. Given 
congruent to line CE 

Now how can I finish this proof paragraph ?

anonymous · Answer

@ganeshie8 @geerky42

wolf1728 · Answer

Angle BCA = Angle DCE (Vertical Angles are equal)
You now have 2 sides and an included angle being equal in 2 triangles.
According to the theorem (side-included angle-side) the triangles are congruent.

anonymous · Answer

So statement 2 would be <BCA = <DCE ?

anonymous · Answer

And the reason would be SAS ? I'm confused ...

wolf1728 · Answer

Yes - they are vertical angles

wolf1728 · Answer

The reason the angles are equal is that vertical angles are always equal.
The triangles are congruent because 2 corresponding sides and an included angle are equal.

anonymous · Answer

so just put vertical angles ?

wolf1728 · Answer

vertical angles are equal

anonymous · Answer

Ok thanks and there is more right ?

anonymous · Answer

statement 3 ?

wolf1728 · Answer

No.  All that you had to prove is 2 corresponding are equal and the included angle is equal.
Statement 3 would be s-a-s (side angle side)

wolf1728 · Answer

left out the word SIDES 
 2 corresponding SIDES are equal

anonymous · Answer

i thought sas was a reason

wolf1728 · Answer

Yes - that's why I said it was statement 3

anonymous · Answer

ok so i'm confused now we dnt have an answer for statement 3

anonymous · Answer

And should line BA is parallel to DE be another statement ?

wolf1728 · Answer

No- if we do this step by step 
BC = CE
and AC = CD (given)

Angle BCA = Angle DCE       vertical angles are always equal.

Triangle ABC is congruent with Triangle DCE   -  s-a-s

anonymous · Answer

ohh ok i see now

wolf1728 · Answer

And here's how Wikipedia defines side angle side:

SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.

anonymous · Answer

Can you answer my other question about line BA and DE please ??

wolf1728 · Answer

I think they are parallel but you don't need to use that for the proof of the triangles being congruent.

anonymous · Answer

Okay thanks so much ! You were a big help

wolf1728 · Answer

Thank you :-)

anonymous · Answer

@shubhamsrg