CPM Homework Help : GC Problem 6-37

Two triangles. The triangle on the left has side lengths of 3 and 6, and one angle of 60 degrees between the two sides. The triangle on the right has side lengths of 3 times the square root of 3 and 6, and one angle of 30 degrees between the two sides. As Samone looked at the triangles at right, she said, “I think these triangles are congruent.” Her teammate, Darla, said, “But they don’t look the same. How can you tell?” Samone smiled and said, “Never trust the picture! Look at the angles and the sides. The measures are all the same.”

Solve for the missing side of each triangle. How do they compare?
Hint (a):
Use the Law of Cosines to solve for the missing sides on each triangle.
Answer (a):
$c = 3\sqrt{3}$
$d = 3$
Are you convinced that Samone is correct? Explain.
Hint (b):
Look at your answers. Is Samone correct? If so, how?
Answer (b):
Samone is correct because the triangles are congruent by $\text{SSS}≅$