Question

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

Answer 1

Here is a copy of the picture and the statements given.

Answer 2

For 5 the reason would be SAS similarity criterion

Answer 3

Do you know what 6 & 7 would be?

Answer 4

as nish states SAS (for similar triangles)
see http://www.regentsprep.org/Regents/math/geometry/GP11/LsimilarProof.htm

Answer 5

once you have shown two triangles are similar then you know
"corresponding angles" are congruent.

Answer 6

finally, if corresponding angles of a transversal are congruent, the lines are parallel

Answer 7

Thanks

Answer 8

Could you also help me with reason 2 & 3? I got those incorrect also. Thanks

Answer 9

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"

Answer 10

reason 2 is not substitution

Answer 11

Can you help with the Converse of the Side Splitter Theorem proof

Answer 12

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)

Answer 13

Thanks.

Answer 14

You're welcome.