anonymous
  • anonymous
Hi I need help with this proof to prove Converse of the Side-Splitter Theorem: Given: XR over RQ = YS OVER SQ Prove: Line RS is parellel to Line XY Thanks
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
Here is a copy of the picture and the statements given.
1 Attachment
anonymous
  • anonymous
For 5 the reason would be SAS similarity criterion
anonymous
  • anonymous
Do you know what 6 & 7 would be?

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phi
  • phi
as nish states SAS (for similar triangles) see http://www.regentsprep.org/Regents/math/geometry/GP11/LsimilarProof.htm
phi
  • phi
once you have shown two triangles are similar then you know "corresponding angles" are congruent.
phi
  • phi
finally, if corresponding angles of a transversal are congruent, the lines are parallel
anonymous
  • anonymous
Thanks
anonymous
  • anonymous
Could you also help me with reason 2 & 3? I got those incorrect also. Thanks
phi
  • phi
I would need a list of the reasons you have learned. in step 2, you add 1 to both sides (in the form RQ/RQ and SQ/SQ) the reason that is ok would read something like " equality remains true when you add equal amounts to both sides" for step 3, you replace XR+RQ with XQ (and also YS+SQ with YQ) the reason would be something like "the whole is the sum of its parts"
mathstudent55
  • mathstudent55
reason 2 is not substitution
anonymous
  • anonymous
Can you help with the Converse of the Side Splitter Theorem proof
mathstudent55
  • mathstudent55
Reason 1. Given Reason 2. A property of proportions Reason 3. Segment addition postulate Reason 4. Congruence of angles is reflexive (this is a theorem) Reason 5. SAS Similarity Reason 6. Definition of similar triangles Reason 7. When two lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel. (this is a postulate)
anonymous
  • anonymous
Thanks.
mathstudent55
  • mathstudent55
You're welcome.

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