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triangle proof
- Thread starter df318
- Start date
df318 said:Given:RP is congruent to RQ
SP is congruent to SQ
Prove: RT bisects PQ
The short version: points R & S are equidistant from P & Q -> they lie on perpendicular bisector to PQ; two points (R & S) determine a single line -> line RS is the perpendicular bisector to PQ & T belongs to the same line -> RT bisects PQ.
If you can't use the theorem about equidistant points then it is longer and involves proving triangle congruence.
There could be other ways as well ...
OK, I will go backwards to show the idea but you are supposed to write it from the opposite end making impression that you always knew where all this going.df318 said:I think it involves proving triangle congruence
To prove that RT bisects PQ you must prove that PT is congruent to TQ. The first is a side of triangle PRT while TQ is a side of QRT. So, you'd need to prove PQT is congruent to QRT. PR is equal to RQ (given) and RT is common to both. The missing part are angles PRT and QRT. Can you take from here?
ok so to prove that angle PRS is congruent to angle QRS, I would state that RS is congruent to itself to prove that triangle PRS is congruent to triangle QRS and then angle PRS is congurent to angle QRS because congruent parts of congruent triangles are congruent.
so with those angles congruent I could say that RT is congruent to itself and that would prove that triangle PRT is congruent to triangle QRT because of SAS
But I don't understand how to prove that RT bisects PQ
so with those angles congruent I could say that RT is congruent to itself and that would prove that triangle PRT is congruent to triangle QRT because of SAS
But I don't understand how to prove that RT bisects PQ
df318 said:and that would prove that triangle PRT is congruent to triangle QRT because of SAS
But I don't understand how to prove that RT bisects PQ
if PRT is congruent to QRT then PT is congruent to TQ making T the midpoint of PQ. Then it follows from definition of bisector that RT bisects PQ; you don't have to prove that RT is perpendicular to PQ as it was not asked.
It is easy though: as two angles at T are congruent (from the same triangles) and they make straight angle together each of them is equal to 180/2 = 90 degrees.
df318 said:OK NOW i get it.. thank you so much :lol:
Glad it was helpful. As I said, if you going to write it do it backwards, starting from proving that triangle PRS is congruent to triangle QRS and so on all the way down to the point in question.