Square Roots and Pythagorean Theorem Chapter 1 Square Roots and Pythagorean Theorem

Square Numbers and Area Models 1.1 Square Numbers and Area Models

Is every square a rectangle? What are descriptors of a rectangle? Is every square a rectangle? Is every rectangle a square? 4 sides 4 right angles What are descriptors of a square? 4 equal sides 4 right angles

The SQUARE....a special type of rectangle 4cm 4cm Area = ??? A = l x w

Congruent the SAME

INVESTIGATE With a Partner from your table..... Which of the following areas can be a square? 4 square units - 12 square units 6 square units - 16 square units 8 square units - 20 square units 9 square units Draw the rectangles on paper…. How many of the above areas were you able to make a square? What are the side lengths of each square How are the side lengths and area related?

This is called a SQUARE NUMBER 81cm2 What is the length of all the sides? This is called a SQUARE NUMBER

4 16 4

Working Backwards…. A square has an area of 225cm2. How long is each side of the square? ? 225 cm2 ? ? ?

Who are the first 3 groups to finish? With one partner at your table... List all the square numbers from 1 to 144. Who are the first 3 groups to 
finish?

The area of my head is 196cm. What is the perimeter?

Practice Questions Pages 8-10 #4b* 5c* 9* 11cd* 14 16 18

1.2 Squares and Square Roots

How can we find Square Numbers? FACTORING 1. Factor 16

INVESTIGATE Factoring…

A number with an odd number of factors is a SQUARE NUMBER! Squaring 5² = 5 x 5 = 52 = 25 Square Rooting

Find the square... 5 5 x 5 25 Find the Square Root 5 5 x 5 25 25

1. Find the square of 6 2. Find the square root of 49

3. What is the square of 9? 4. What is the square root of 9

Which of the following are square-able? 4 5 578 9 0 12 34

Which ones are square rootable? 48 49 52 56 64 68 82 84 99 
100 110 114 121 140 144 152 
164 168 169

Practice! 5d* 6c* 7cd* 11ad* 14cd* 15b* 17 Page 15 - 16 Read Carefully! Page 15 - 16 5d* 6c* 7cd* 11ad* 14cd* 15b* 17

Measuring Line Segments 1.3 Measuring Line Segments

INVESTIGATE Without using a ruler, find the area and the side length of each square.

1.

2. What are the side lengths of these squares?

Questions.. Pages 20-21 3af* 4bde* 5ac* 7c* 8b 10a

1.4 Estimating Square Roots

From last class…What is the side length?

INVESTIGATE 2 11 18 5 24 NO CALCULATORS! 1) Place each square root on the number line below 2) Write the estimated square root as a decimal 2 11 18 5 24 NO CALCULATORS!

Estimating the square root of a decimal 84.5 84.5 is between which two perfect squares? ____ and _____

Example 1. How can we estimate? 29 It is between ___ & ___ Which means it’s between what two whole numbers? ___ & ___

Example 2. Which whole number is 115 closest to?

Example 3.

top of the previous layer is 2 cm less in side Example 4. This is a four layered wedding cake. The area of the bottom cake is 324cm². If the cake on top of the previous layer is 2 cm less in side length, what is the area of the top layer?

4cd* 5bd* 6(Just Estimate) Work on your roots... Page 25 -26 4cd* 5bd* 6(Just Estimate) 9c* 10b* 13c 16

1.5 The Pythagorean Theorem

INVESTIGATE Make an equation using these symbols. The answer must be 10

The “Right” Triangle ? What does 
this mean?

His theorem was.... a² + b² = c² c a b

C is ALWAYS the Hypotenuse A & B are interchangeable

What is the length of the hypotenuse? Example 1. What is the length of the hypotenuse? 6 cm 7cm

Example 2. What is the height of the triangle?

Example 3. The height of this house is 24 feet and the width of the house is 28 feet. What is the length of one side of the roof?

Example 4.

Example 5. How far is the ladder from the wall? **Which side is c?

Practice Pages 34 - 35 5a*d* 6a*b* 7b*c 8a 13ab c2 - b2 = a2

Exploring the Pythagorean Theorem 1.6 Exploring the Pythagorean Theorem

What types of triangles are these? Do you think we can use the theorem for all of these triangles?

INVESTIGATE Record your results as follows… What do we notice?

Are the following triangles right triangles? 
How do we know? Example 1) 7cm, 7cm, 81cm Example 2) 7cm, 24cm, 25cm

When three numbers satisfy the Pythagorean Theorem, these numbers are called... PYTHAGOREAN TRIPLES

Which of these sets of numbers is a Pythagorean Triple? Example 3. 8, 15, 18 Example 4. 11,60, 61

Practice Page 43 - 45 3a*b 6a*d*g* 7f* 8 12d 14

1.7 Applying the Pythagorean Theorem

REVIEW from last class... 6 12 Are 8,15,17 Pythagorean Triples? What is the length of the unknown side? 6 12 Are 8,15,17 Pythagorean Triples?

Example 1.

Example 2.

Example 3. How long is this line?

Example 4. A sloped mountain road is 13 km long. It covers a horizontal distance of 9 km. What is the change in elevation of the road? Give your answer to one decimal place.

Example 5. In shop class, you make a table.  The sides of the table measure 36" and 18".  If the diagonal of the table measures 43", is the table “square”? 

Example 6 What is the width?

Practice Pages 49-51 5b* 6* 8a*b* 9 15 16