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GEOMETRY�

TERM 2

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Table of Contents

Page #	Title	UNIT

# Pythagorean Theory GS

#

Pythagorean Theory

GS

DO IT NOW

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PYTHAGOREAN THEORY

is changing to

“RIGHT ANGLE

TRIANGLE THEORUM”

Because it has been discovered that he may not have been the first person to have actually discovered it, but is the first person recognized to have found it… likely due to the colour of his skin?

aka

“RATT”

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Pythagoras doesn’t know what to do next

Help Pythagoras discover his formula

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3x3 = square

OR 3²= square

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Upon completing this lesson �you will be able to:

Identify sides of Right Triangle as either Legs or Hypotenuse
Explain the Pythagorean Theorem
Apply Pythagorean Theorem to find length of the sides of Right Triangles

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RIGHT TRIANGLE

90°

LEG

HYPOTENUSE

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PYTHAGOREAN THEOREM

90°

LEG

HYPOTENUSE

a²+ b² = c²

a

b

c

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PYTHAGOREAN THEOREM

Legs

Two sides (a and b) that form the right angle

Hypotenuse

Side opposite the right angle; called c

Formula

a² + b² = c²

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TRY IT

Identify the sides of each triangle as either legs or hypotenuse

(assume all shapes are right triangles)

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3²= 3 x 3

4²= 4 x 4

5²= 5 x 5

= 9

= 16

= 25

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a²+ b² = c²

3²+ 4² = c²

9+ 16 = c²

25 = c²

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WE NEED TO GO BACK IN TIME!

REMEMBER?

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ALGEBRA DEFINITION

INVERSE

RECIPROCAL

REMEMBER?

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REMEMBER?

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REMEMBER?

OPPOSITE OF

+

IS

–

OPPOSITE OF

x

IS

÷

OPPOSITE OF

x²

IS

√

SQUARE ROOT

EXPONENTS

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SQUARE ROOT

A square root of a number is a value that can be multiplied by itself to give the original number.

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a²+ b² = c²

3²+ 4² = c²

9+ 16 = c²

25 = c²

5 = c

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a=1400m

b=5000m

c=?

2km

7km

?

6mm

3mm

?

a=1cm

b=9cm

c=?

a=6.4km

b= ?

c=120.17km

TRY IT

(assume all shapes are right triangles and Show Your Work)

b)

a)

c)

d)

e)

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a=2km

b=7km

c=?

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SOLVING FOR A LEG

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a=6.4km

b= ?

c=120.17km

e)

a²+ b² = c²

6.4²+ b² = 120.17²

40.96+ b² = 14,440.8289

b² = 14,399.8689

√b² = √14,399.8689

b = 119.99km

-40.96

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a=6.4km

b= ?

c=120.17km

e)

a²+ b² = c²

b² = c² - a²

-a²

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TECH CENTRE

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https://quizizz.com/admin/quiz/57d85113ff0b92c507e98f61

QUIZZIZ ACTIVITY

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TECH

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bit.ly/stavmathjournal

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Cirque De Soleil is setting up a large tent for their amazing show!

Two poles, QU and RT, are placed perpendicular to the ground and 12m apart.

Pole QU is 4m in length and pole RT is 7.5m�in length.

A tarp is placed over the poles and secured to the ground at P, 3m from the base of pole QU, and S, P 3 U 12 4 m from the base of pole RT.

Determine P Q + QR + RS, the length of the tarp.

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3cm

5cm

What is the length of the red line?

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3cm

5cm

What is the length of the red line?

3

2

3 + 5 = 8

c²= 8^{2 +}2²

c²= 64 + 4

c²= 68

√c²= √68

c = 8.246 cm

ANSWER

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You can use The Pythagorean Theorem to solve many kinds of problems.

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Suppose you drive directly west for 48 km,

48

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Then turn south and drive for 36 km.

48

36

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How far are you from where you started?

48

36

?

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48²

Using The Pythagorean Theorem,

48

36

c

36²

+

=

c²

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Why?

Can you see that we have a right triangle?

48

36

c

48²

36²

+

=

c²

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Which side is the hypotenuse?

Which sides are the legs?

48

36

c

48²

36²

+

=

c²

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Then all we need to do is calculate:

c²= 48^{2 +}36²

c²= 2304 + 1296

c²= 3600

c²= √3600

c = 60

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So you end up 60 km from where you started.

48

36

60

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