warm-up 1)the sum of three consecutive odd integers is 111. what is the smallest number? 2) write an...

Warm-Up1) The sum of three consecutive odd

integers is 111. What is the smallest number?

2) Write an expression for: Nine more than the quantity x plus 5

3) Solve & graph : 21 – 5r < 3r + 45

HW Check – Equation Word Problems

FORMULAS

Pythagorean Theorem & Distance

The Pythagorean Theorem

Remember right triangles?

Special Names for Right Triangles

Hypotenuse!

Legs!

The Pythagorean Theorem

In any right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.

a

b

c

a2

ac

b

+ b2 = c2

+ =a2b2 c2

1) Find the length of the unknown side of the triangle:

8m

15 m

2) Find the length of the unknown side of the triangle:

5 y12 y

Pythagorean Triples

Three side lengths that would form a right triangle.

Ex) 3) Are the following side lengths Pythagorean triples?

a) 8, 4, 10 b) 3, 4, 5

4) How far does the catcher have to home plate?

Literal Equations

A literal equation is an equation with more than one variable. Formulas are literal equations.

Sometimes we need to solve a formula for a specific variable

Ex 5) Solve for b.

6) Which 3 of the following side lengths could be used to create a right triangle?

11, 5, 12, 9, 13

Word Problems

7) John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

8) A 13 foot ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the wall is 13 feet Will the ladder reach the top of the wall?

. (4, 6)

.(-3, -2)

9) How can we find the distance between the two points?

How long is this leg?

What about this leg?

We can use the Pythagorean Theorem!

. (4, 6)

.(-3, -2)

The Distance FormulaThe distance formula uses the Pythagorean Theorem to find the distance between two points.

It has the coordinates for each point built in, so it finds the length of each “leg” for you!

. (4, 6)

.(-3, -2)

The Distance Formula

Use the distance formula to find the distance between the two points.

. (3, -4)

.(-5, 5)

10)

Use the distance formula to find the distance between the two points.

Word Problem

11) On a map’s coordinate grid, Walt City is located at (-1, -3) and Smithville is located at (4, 9). How long is a train’s route as the train travels along a straight line from Walt City to Smithville? (One map unit equals one mile.)

CW:Pythagorean Theorem

& Distance Formula

Coming up…

HW tonight – 1.6

QUIZ Thursday!