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.

Unit 6: Geometry

Group Area of Square with side a Area of Square with side bArea of Largest Square with

side cType of Triangle

         

         

         

         

         

         

         

         

Unit 6: Geometry

Learning Goals

I can use the Pythagorean Theorem to solve right angle triangles

Lesson Three: Pythagorean Theorem

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: a2 + b2 = c2 Where c is

ALWAYS the hypotenuse of the longest side.

a

b

c

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

Square Rooting

3

4

c

Unit 6: Geometry

Lesson Three: Pythagorean Theorem

Example 1: Find the value for c

Unit 6: Geometry

Lesson Three: Pythagorean Theorem

1.5

2.5

x

Example 3: Determine the value of the unknown side

Unit 6: Geometry

Lesson Three: Pythagorean Theorem

The Pythagorean Theorem can help us to find unknown measurements in various shapes.

The length and width of a rectangle are 12 cm and 15 cm. Calculate the length of the diagonal.

15 cm

12 cmdd 2 = 152 + 122 d 2 = 225 + 144 d 2 = 369

369d

d = 19.2 cm

c2 = a2 + b2

Tanya is making a party hat using a cone made out of paper. Determine the height of the cone.b2 = c2– a2

h2 = 144

h = 12 cm

h2 = 132– 52 h2 = 169– 25

144h

h

5 cm

13 cm

Unit 6: Geometry

Lesson Three: Pythagorean Theorem

Practice

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