Jayda G.

asked • 10/18/22

Proof for line segmants

What is the poof of, given: AB is congruent to DE; C is the midpoint of BD. Prove: AC is congruent to CE

Paul M.

tutor
Where are these points located, i.e. what is the geometric relationship of the points?
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10/18/22

Patricia D.

tutor
Do you have a diagraam? Have you started the proof? show me what you have, and I will help guide you with this.
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10/18/22

Philip P.

To prove AC is congruent to CE, you must first prove that triangle ABC is congruent to triangle EDC. Then AC will be congruent to CE by CPCTC (corresponding parts of congruent triangles are congruent). We are one piece of information short of proving the two triangles are congruent. We know AB is congruent to CE (given) and BC is congruent to DC (definition of midpoint). Now we need to have one angle congruent to the corresponding angle in the other triangle - that's the info that's missing. Is DE parallel or perpendicular to AB?
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10/19/22

Mark M.

Philip P. I do not read any indication that this refers to a triangle.
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10/21/22

Reuben B.

tutor
One important piece of information that I would suggest to help you with proofs in general is that when you see a vocab word, that you think about defining what that vocabulary word means. For instance, if you see the term "midpoint," you can translate C is the midpoint of BD as C is the halfway point between B and D. This means that CB has to be congruent to CD. The piece of information might be useful to you as you create your proof.
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10/28/22

1 Expert Answer

By:

Churchill A. answered • 11/12/22

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5+ Years of Tutoring Experience with Geometry
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  1. Given [AB bar is congruent to DE bar]
  2. A--B is congruent to D--E
  3. Given [C = BD Midpoint]
  4. BC = CD -> BC bar is congruent to CD bar [Congruence Definition]
  5. B--C is congruent to C--D
  6. (AB + BC) = (CD + DE)
  7. (AB + BC) = AC [Segment Addition]
  8. (CD + DE) = CE [Segment Addition]
  9. Since (AB + BC) = (CD + DE), Therefore AC = CE
  10. AC = CE -> AC bar is congruent to CE bar [Congruence Definition]
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