Warm Up 23 x 2 6 x 2

Warm Up • -2(3 x+ 2) > 6 x + 2 • Write an equation such that you have to subtract 3 and multiply by 4 when solving. Solve the inequality. • Compare inequalities and equations.

Day 5 and 6 Apply the Pythagorean Theorem and Use the Distance Formula

PERIGAL’s PUZZLE There are hundreds of proofs of the Pythagorean Property. * The proof you will investigate is Perigal’s Puzzle. Henry Perigal, a Londoner, discovered this interesting demonstration of a geometric proof in 1830. The four parts of Square B together with Square A fit exactly on Square C. Cut out Squares A and B, cut Square B into its four parts and see if you can do it. QUESTIONS: • How does this demonstration show that the Pythagorean Property “works” for the triangle that is framed by the three squares? • Will the same procedure work for any other right triangle? How could you find out? Use the following steps to see if it “works” for another triangle: • Construct a right triangle whose sides are not the same length as the one below. • Construct squares on all three sides of your triangle. • Mark the center of the two smaller squares.

Notes on Pythagorean Theorem • The ______________ describes the relationship of the lengths of the sides of the triangle. • Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2+b 2=c 2 b c

Example: What is the length of the hypotenuse of the triangle below? a= 9 a 2+b 2=c 2 92+122=c 2 81+144=c 2 c b = 12 15 = c The length of the hypotenuse of a right triangle is 15 cm.

What is the length of the hypotenuse of a right triangle with legs of lengths 7 cm and 24 cm? • Hint: Draw a picture.

Example #1 You are playing your favorite gold course. To get from point A to point B you must avoid walking through the pond. To avoid the pond you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

Example #2 In a computer catalog, a computer screen is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch?

Exit Ticket Find the missing side length for the right triangle. 1. a=3, b=4, c= ___ a c 2. a=8, b= ___, c=10 3. a = ___, b= 40, c=50 b 4. Use the Pythagorean theorem to find the distance between (-1, 1) and (3, -2). Note: Corrections on HW Please make sure you are coming to tutorial. Test is coming up soon! Are you ready?

Day 6 Solve the following 1. ax+b= c for x 2. Cx+pq- t= e for q

Homework

Distance Formula The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points. The subscripts refer to the first and second points; it doesn't matter which points you call first or second. x 2 and y 2 are the x, y coordinates for one point x 1 and y 1 are the x, y coordinates for the second point d is the distance between the two points

Practice • Find the distance between the points (– 2, – 3) and (– 4, 4).

You Try Find the distance between the points(3, -3) and (11, 3).

Midpoint The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments. The Midpoint Formula: The midpoint of a segment with endpoints (x 1 , y 1) and (x 2 , y 2) has coordinates

Example: Find the midpoint

Your Turn: Find the Midpoint 1. (-2, 4) and (5, 7) 2. (-3, -4) and (4, 5)

M is the midpoint of CD. The coordinates M(-1, 1) and C(1, -3) are given. Find the coordinates of point D.

Slope Review slope is a ratio and can be expressed as: change in y over change in x. or or Example: Find Slope of (-4, 4) and (8, -2)

Your Turn 1. Find the slope of (-3, 4) and (5, 6) 2. Find the slope of the graph.

Please wait to hear all directions MATH RELAY!!!

#1 A baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest 10 th of a foot, between 1 st base and 3 rd base?

#2 A suitcase measures 24 inches long and 18 inches high. What is the diagonal length of the suitcase to the nearest 10 th of a foot?

#3 Oscar’s dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dogs house, in feet, at its tallest point?

#4 John leaves school to go home. He walks 6 blocks north and then 8 blocks west. How far is John from the school?

#5 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?

#6 The rectangle PQRS represents the floor of a room. 2 m P Q A 4 m S 12 m Ivan stands at point A. Calculate the distance of Ivan from a) the corner R of the room b) the corner S of the room R

#7 A can of drink is in the shape of a cylinder with a height of 15 cm and radius 4 cm. What is the length of the longest straw that will fit inside the can?

#8 Scott wants to swim across a river that is 400 meters wide. He beings swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point?

#9 In construction, floor space must be given for staircases. If the second floor is 3. 6 meters above the first floor and a contractor is using the standard step pattern of 28 cm of tread for 18 cm of rise then how many steps are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase?

#10 In the Old West, settlers often fashioned tents out of a piece of cloth thrown over tent poles and then secured to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 4 meters high and 3 meters wide?

ANY QUESTIONS?

Homework Packet Page 6 Reminder- tutorials are Monday and Thursday 1 st half of lunch *You need 2 lunch tutorials

You try! Using graph paper find the length of each side, the area, and the perimeter of the polygon formed by the following points. 1) (-3, 6) (5, -5) and (-3, -5) d 1= d 2= d 3= A= 2) (-4, -2) (-4, -6) (4, -6) d 1= d 2= A= P= d 3= d 4= 3) (-3, 3) (4, 3) (-4, -3) (3, -3) d 1= d 2= A= P= d 3= d 4= d 3= A= 4) (1, 3) (-2, -3) (4, -3) d 1= d 2= P= P=