SOLUTION: Two triangles are drawn on a paper and labeled DEG and POM. The lengths of DE and OM are congruent. The lengths of EG and PM are congruent. What additional piece of information do

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Question 1152603: Two triangles are drawn on a paper and labeled DEG and POM. The lengths of DE and OM are congruent. The lengths of EG and PM are congruent. What additional piece of information do you need to prove the triangles are congruent by SAS? Draw the triangles in such a way that you are able to prove they are congruent.
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!

With the given info that DE = OM, and that EG = PM, we can draw this out.

The segments with the single tickmark are the same length.
The segments with the double tickmarks are the same length.

The angles E and M are between the segments mentioned above. So this is the missing piece of info if we wanted to use SAS.

If angle E = angle M, then we can use SAS to prove the triangles congruent.
More technically, if we knew that angle DEG = angle OMP, then we can use SAS to prove the triangles congruent.

Here is an updated drawing

If we know the green angles are the same measure, then we can use SAS to prove the triangles congruent.

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

See the lessons
    - Congruence tests for triangles
    - Problems on congruence tests for triangles
    - Problems on congruence tests for triangles-2
in this site to learn about congruence tests for triangles and assosiate problems.

Regarding the terminology in your post, notice that this phrase "The lengths of DE and OM are congruent" is not correct.

The correct way to express it is to say "the lengths are EQUAL".

Or to say "the segments are congruent".

But not "the lengths are congruent" - this form is NEVER used.

Happy learning (!)