1. 1) Create three squares, one for each of the side lengths given on the card you received. 2) Cut out the squares. 3) Position the three squares on the blank paper so that the three squares create a triangle in the middle (see diagram). 4) Glue the squares into position, carefully lining up the corners. Do not allow the corners to overlap or have gaps. 5) Label the area of each square inside the square. 6) Trace the sides of the triangle in marker. 7) Measure the angles in the triangle and record the measures on the diagram.

2. Unit 6: Geometry GroupArea of Square with side aArea of Square with side b Area of Largest Square with side c Type of Triangle

3. Unit 6: Geometry Learning Goals  I can use the Pythagorean Theorem to solve right angle triangles Lesson Three: Pythagorean Theorem

4. Unit 6: Geometry Lesson Three: Pythagorean Theorem In a right triangle two sides are perpendicular to each other and the third side is the longest side. We can label the two perpendicular sides a and b (doesn’t matter which) and the third side (longest side) c. The longest side is also known as the hypotenuse. The Pythagorean states: a 2 + b 2 = c 2 Where c is ALWAYS the hypotenuse of the longest side. a b c

5. Unit 6: Geometry Lesson Three: Pythagorean Theorem To solve a problem involving Pythagorean Theorem we need to get the variable by itself. Since the variable in Pythagorean Theorem is always squared, we need to undo the squaring. The inverse (opposite) of adding is…. The inverse (opposite) of multiplying is…... The inverse (opposite) if squaring is……. Subtracting Dividing

6. 3 4 c Unit 6: Geometry Lesson Three: Pythagorean Theorem Example 1: Find the value for c

7. Unit 6: Geometry Lesson Three: Pythagorean Theorem 1.5 2.5 x Example 3: Determine the value of the unknown side

8. Unit 6: Geometry Lesson Three: Pythagorean Theorem The Pythagorean Theorem can help us to find unknown measurements in various shapes.

9. The length and width of a rectangle are 12 cm and 15 cm. Calculate the length of the diagonal. 15 cm 12 cm d d 2 = 15 2 + 12 2 d 2 = 225 + 144 d 2 = 369 d = 19.2 cm c 2 = a 2 + b 2

10. Tanya is making a party hat using a cone made out of paper. Determine the height of the cone. b 2 = c 2 – a 2 h 2 = 144 h = 12 cm h 2 = 13 2 – 5 2 h 2 = 169– 25 h 5 cm 13 cm

11. Unit 6: Geometry Lesson Three: Pythagorean Theorem Practice  Page 27 #4ac, 5, 7  Page 211 #4ac  Page 213 #15