Question 486577: I have a triangle with sides of 3, 4, and 5, and angles of 30° and 60°. Which of the following would be congruent to it? (You will need to use what you've learned about triangles and angle / side relations, as well as your knowledge of the rules of congruence to fill in the gaps and answer the question. Sketches may be helpful.)
A a triangle with angles of 30°, 60°, and 90°
B an angle of 90°
C a triangle with sides of 6, 8, and 10
D a triangle with sides of 3 and 4
E a triangle with a side measuring 4, next an angle of 90°, and next a side measuring 3
F a triangle with a side measuring 3, next an angle of 60°, and next a side measuring 4
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! The third angle will be 90 degrees, as the three will add to 180 degrees.
A This will not necessarily be a congruent triangle. The angles are congruent, so the triangles are similar.
B. An angle of 90 degrees is congruent to the corresponding 90 degree angle.
C. The sides would be similar but not congruent.
D. Those parts would be congruent, but not necessarily the triangles.
E. Yes, and by the SAS theorem, the two triangles will be congruent.
F. No, for the SAS theorem you need the two sides and the included angle, the 60 degree angle will not be the included angle.
Cleomenius.
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