SOLUTION: How do you find out if two triangles are similar? I know that the triangles' angles must be congruent, and their sides must be proportional. How do you determine if the sides are p

Question 184450: How do you find out if two triangles are similar? I know that the triangles' angles must be congruent, and their sides must be proportional. How do you determine if the sides are proportional?
Here is the problem:
Are any of these triangles similar? If so, write the appropriate similarity statement.
1st triangle-CAB CA=4; CB=4; AB=5/angles A and B are congruent.
2nd triangle-PRQ PR=8; RQ not listed; QP=10
3rd triangle-XYZ XZ=8; XY not listed; ZX=8
On triangles PRQ and XYZ, angles Z and P are congruent.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you have two triangles that have 2 congruent angles, then the third angles must be congruent because the angles of a triangle always sum to 180. If you have three congruent angles, then the sides must be related with a common constant of proportionality and therefore are at least similar (congruent if the constant of proportionality is 1)

John

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