Eighth Grade - MATH
3: Math
Unit 6: Geometry
Lesson 9
Using the Pythagorean Theorem
Students are instructed to draw horizontal and vertical segments between two points to create a right triangle and to treat the diagonal connecting the points as the hypotenuse. Students work through explicit coordinate examples (A(0,0) and B(6,8); A(−1,2) and B(2,−2)) where they determine the horizontal and vertical distances (6 and 8; 3 and 4) and apply a^2 + b^2 = c^2 to find the distance. Students complete a "Grid Problems" activity page with multiple coordinate-pair exercises that require plotting points, measuring the legs, and computing the hypotenuse as the distance.
Lesson 11
Unit 6 Test
The Parent Plan skills list explicitly includes "Apply the Pythagorean Theorem to find the distance between two points in a coordinate system." Students solve several Pythagorean problems (e.g., find hypotenuse for legs 6 and 8, legs 9 and 12, and verify right triangles like 10, 24, 26). The unit contains many coordinate-plane exercises with given vertex coordinates, reflections, rotations, translations, and a dilation problem with explicit coordinates (e.g., triangles A(2,3), B(4,8), C(6,4) and A'(4,6), B'(8,16), C'(12,8)).
Unit 9: Semester Exams
Lesson 7
Geometry Review
Students are asked to find the distance between the points A(0, 0) and B(6, 8) and to "Show your work using the Pythagorean Theorem." Students are prompted to "Write the formula for finding the distance between two points," which requires expressing d = sqrt((x2-x1)^2+(y2-y1)^2). Students are directed to a supporting video titled "Using Pythagorean Theorem to Find the Distance Between Two Points," reinforcing the same procedure.
Lesson 10
Semester Exam
Problem 16 asks students to "Find the distance between the points A(0, 0) and B(6, 8)." The answer key gives the distance as 10 units, demonstrating the expected result of using a right-triangle relationship on the coordinate plane. Problem 17 additionally asks students to find a hypotenuse given legs of 9 and 12, providing direct practice with the Pythagorean Theorem.
