Using the Pythagorean Theorem in 3-Dimensional Shapes

43210 In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.  Make connection with other content areas.  Explain the relationship between the Pythagorean Theorem and the distance formula. The student will understand and apply the Pythagorean Theorem.  Prove the Pythagorean Theorem and its converse.  Apply the Pythagorean Theorem to real world and mathematical situations.  Find the distance between 2 points on a coordinate plane using the Pythagorean Theorem. The student will understand the relationship between the areas of the squares of the legs and area of the square of the hypotenuse of a right triangle.  Explain the Pythagorean Theorem and its converse.  Create a right triangle on a coordinate plane, given 2 points. With help from the teacher, the student has partial success with level 2 and level 3 elements.  Plot 3 ordered pairs to make a right triangle  Identify the legs and the hypotenuse of a right triangle Find the distance between 2 points on the coordinate grid (horizontal and vertical axis). Even with help, students have no success with the unit content. Focus 5 - Learning Goal #1: Students will understand and apply the Pythagorean Theorem.

Pythagorean Theorem Review The Pythagorean Theorem states: in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. a 2 + b 2 = c 2 Find the length of AC in the diagram below: c b a a = 13 2 a = 169 a 2 = 144 a = 12

3-Dimensional Figures How would you find the length of segment AV? Do you see a right triangle inside the shape? How would you find the length of segment AF? Do you see the right triangle inside the shape? 5 m 12 m

Use the Pythagorean Theorem to find the length of diagonal AV. To find AV we need the lengths of sides AM and MV. What is the length of MV? What is the length of AM? We have enough information to solve the problem. a 2 + b 2 = c = c = c = c 2 13 = c 5 m 12 m 5 m The length of diagonal AV is 13 m.

Use the Pythagorean Theorem to find the length of diagonal AF. AF is the diagonal going through a prism. To find AF, we use the Pythagorean Theorem differently. To find AF we need to know the length, width and height of the prism. What is the length = AB? What is the width = FG? What is the height = GB? (length) 2 + (width) 2 + (height) 2 = (diagonal of prism) = d = d 2 49 = d 2 7 = d 6cm G 2 cm 3 cm The length of the diagonal AF is 7 cm.

Use the Pythagorean Theorem to find the length of diagonal TX. 12 in 6 in 9 in