Module 7, Topic C revisits the Pythagorean Theorem and its applications, now in a context that includes the use of square roots and irrational numbers. Students learn another proof of the Pythagorean Theorem involving areas of squares off of each side of a right triangle (8.G.B.6). Another proof of the converse of the Pythagorean Theorem is presented to students, which requires an understanding of congruent triangles (8.G.B.6). With the concept of square roots firmly in place, students apply the Pythagorean Theorem to solve real-world and mathematical problems to determine an unknown side length of a right triangle and the distance between two points on the coordinate plane (8.G.B.7, 8.G.B.8).