Question 467387: R,S, and T are the vertices of one triangle. E, F, And D are the vertices of another triangle. Measurement Of angle R = 60, Measurement of angle S = 80, Measurement of angle F = 60, Measurement of angle D = 40, and EF = 4. Are the triangles congruent? if yes, explain and tell which statement is congruent to RT
a) yes, by ASA; FD
b) yes, by ASA; ED
c) yes, by SAS; ED
d) No, the two triangles are not congruent
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Best answer d). In fact the two triangles could be congruent, but you can't prove it. And you can't actually prove that they are not congruent either (unless the difference in size as they are drawn is clearly and measurably different). They are, in fact similar. But you are only told that EF = 4, and you have no idea of the measure of the corresponding side of RST. All you can do, because you know that the three angles must all be equal in measure to their corresponding angles, R and F, S and E, T and D, is say that the two triangles are similar
John
My calculator said it, I believe it, that settles it
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! these triangles are similar by AA.
you cannot conclude they are congruent because you only have the length of one side of one of the triangles and do not have the length of the corresponding side on the other triangle.
to correctly synchronize the triangles, you should label them as follows:
triangle RST is similar to triangle FED
angle R is equal to angle F (60 degrees)
angle S is equal to angle E (80 degrees)
angle T is equal to angle D (40 degrees)
since the sum of the angles of a triangle is always equal to 180 degrees, the missing angle in each triangle was found by subtracting the sum of the 2 known angles from 180 to get the measurement of the missing angle.
you state that EF = 4.
in order to prove congruence, RS must also have been equal to 4.
i did not see a statement that provided that information.
draw your triangle RST and FED as follows:
R is on the left of triangle 1
F is on the left of triangle 2
S is top middle of triangle 1
E is top middle of triangle 2
T is on the right of triangle 1
D is on the right of triangle 2
plug in angle values and side values where known.
you'll see that all the corresponding angles are equal and that side EF = 4 but there is no information about the size of corresponding side RS.
you can conclude the triangles are similar but you can't conclude that they are congruent.
your answer has to be selection d.
all the other answers are clearly false since not enough information has been given to allow you to prove that.
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