Question 934933: given: A(3,-1), B(5,2), C(-2,0), p(-3,4), Q(-5,-3), R(-6,2)
Prove:angle ABC is congruent to angle RPQ
Found 2 solutions by jim_thompson5910, AnlytcPhil:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If triangle ABC is congruent to triangle RPQ, then you can prove it to be true using the SSS congruence property. This is after you find the lengths of these segments
AB, BC, AC
RP, PQ, RQ
use the distance formula to find each length above. Once you show that AB = RP, BC = PQ, AC = RQ, then you can the SSS congruence property to prove that triangle ABC is congruent to triangle RPQ.
Once you know triangle ABC is congruent to triangle RPQ, then you can use CPCTC to show that angle ABC is congruent to angle RPQ.
Note: CPCTC = corresponding parts of congruent triangles are congruent
Answer by AnlytcPhil(1810)  (Show Source):
You can put this solution on YOUR website!
I'll try to do a little more for you here than the other tutor,
although what he says is very correct.
A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2)
To do such problems you must draw graphs, like this:
Only by drawing the graph, can you determine what you need
to do.
You must use the distance formula:
  
You must use it 6 times to show that
AB = RP
AC = RQ
BC = PQ
Here is how you show AB = RP
     
  
Now do the same to show AC = RQ and BC = PQ.
Then the two triangles are congruent by SSS.
Edwin
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