Finding Distance by using the Pythagorean Theorem Focus

Finding Distance by using the Pythagorean Theorem

Focus 5 - Learning Goal #1: Students will understand apply the Pythagorean Theorem. 4 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. 3 The student will understand 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. 2 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. 1 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). 0 Even with help, students have no success with the unit content.

What is the Pythagorean Theorem?

What is the distance between (-2, 1) and (1, 5)? • Draw a line connecting the points. • Draw in lines that would make a right angled triangle, using these two points as corners.

What is the distance between (-2, 1) and (1, 5)? • Find the length of the horizontal side. (subtract the x’s = 1 – -2) • 3 • Find the length of the vertical side. (subtract the y’s = 5 -1) • 4 4 3

What is the distance between (-2, 1) and (1, 5)? • Use the Pythagorean Theorem to find the missing side. • a 2 + b 2 = c 2 • 32 + 42 = c 2 • 9 + 16 = c 2 • 25 = c 2 c 4 3

What is the distance between (-6, 6) and (1, -4)? 10 c 7 • Draw in the line to connect the dots. Draw in the horizontal and vertical lines. • Find the lengths of the horizontal and vertical lines. • Horizontal 1 - -6 Vertical -4 - 6

What is the distance between (-6, 6) and (1, -4)? 10 • Use the Pythagorean Theorem to find the missing side. • a 2 + b 2 = c 2 • 102 + 72 = c 2 • 100 + 49 = c 2 • 149 = c 2 c 7