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Question 419738: The following triangles, ABC and DEF are congruent.
on triangle ABC:
Angle ABC is a 90 degree angle (I think)
BC = 24cm
CA = 40cm
Angle ACB = 53.1 degrees
on triangle DEF:
Angle DEF is a 90 degree angle ( I think)
ED = 32cm
Angle EDF is 36.9 degrees
Find the lengths of all missing sides and measures of all angles for both triangles. Include correct units with each of your answers.
First Triangle (ABC):
side AB =
angle BAC =
angle ABC = 90 ?
Second Triangle (DEF):
side DF =
side EF =
angle DEF = 90 ?
angle EFD =
My answers keep fluctuating and I am a little confused on the formulas. Any help would be GREATLY appreciated!!! Maybe if you could show me how you came to get the answers that would be great! Thank you so much!
Answer by duckness73(47)   (Show Source):
You can put this solution on YOUR website! If the triangles are congruent, then when they are "overlayed" they should match up exactly. That means that each triangle has a 90 degree angle, a 53.1 degree angle, and a 36.9 degree angle. It also means that each triangle has a 40cm side, a 24 cm side, and a 32 cm side. So, for each triangle, you can look at what you are missing, and get the information that you are missing from the other triangle.
First Triangle (ABC):
side AB = 32 cm (from triangle DEF side DE)
angle BAC = 36.9 degrees (from triangle DEF angle EDF)
angle ABC = 90 ? Yes, you can verify this using the Pythagorean Theorem
Second Triangle (DEF):
side DF = 40 cm (from triangle ABC side AC)
side EF = 24 cm (from triangle ABC side BC)
angle DEF = 90 ? Yes, you can verify this using the Pythagoriean Theorem
angle EFD = 53.1 degrees (from triangle ABC angle ACB)
Pythagoriean Theorem says that  where c is the length of the side opposite the right angle and a & b are the lengths of the other two sides. Therefore, you have
 meaning that you have a right triangle and angle ABC and angle DEF are 90 degrees.
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