Warm Up Find what numbers the following values are in between. 1. 30 2. 14 3. 55 4. 48
Color squares on each side of the triangles with map pencils. Remember A square has 4 equal sides!
Looking back at the Triangle exploration Activity what is the pattern that you see for y 13 Right Triangles? 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 x What is the relation between the 3 sides of the triangle?
The Pythagorean Theorem Learn to use the Pythagorean Theorem and its converse to solve problems. Course 3
Vocabulary Pythagorean Theorem leg hypotenuse
Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.
A squared plus b squared equals c squared.that s Pythagorean Theorem! A squared plus b squared equals c squared.that s Pythagorean Theorem! A is the leg that touches the right angle, B is the leg that Touches the right angle, C connects A and B, it s the longest side the name we give C is the HYPOTENUSE!
Hypotenuse a (Always the longest side!) Legs b
Formula: Substitute: Evaluate Exponents: Add: Is it Right? a)9, b)10, c)11
a)5, b)7, c)12 Formula: Substitute: Evaluate Exponents: Add: Is it Right?
a=6 b= 8 c= 10 Formula: Substitute: Evaluate Exponents: Add: Is it Right?
a=5 b = 12 c=13 Formula: Substitute: Evaluate Exponents: Add: Is it Right?
Practice Which one is not a right triangle? A 18 cm, 24 cm, 30 cm B 12 cm, 16 cm, 21cm
What next?? We will use the Pythagorean Theorem to find the missing sides of a Right Triangle!!!!
6 cm x Formula: Substitute: Solve: 8 cm
4 5 c Formula: Substitute: Solve:
5 7 c Formula: Substitute: Solve:
b = 8 c a = 15 Formula: Substitute: Solve:
12 cm 20 cm Formula: Substitute: Solve: x
25 b Formula: Substitute: Solve: 7
k 3 cm 8 cm Formula: Substitute: Solve:
12 4 b Formula: Substitute: Solve:
1) 2)
Pythagorean Theorem & Real world Applications!! Today we are going to use Pythagorean theorem to do word problems!!! Remember to write down the steps!!
A carpenter braces an 8-foot by 15-foot wall by nailing a board diagonally across the wall. How long is the bracing board? Formula: Substitute: Draw Picture: Solve:
Justine rides her bike 3 miles to the east and then 10 miles to the south. How far is she from her starting point? Draw Picture: Formula: Substitute: Solve:
The Tetherball Accident 5 ft 10 ft Mario and his youngest sister, Alexis, were playing tetherball in their backyard. Alexis was standing approximately 5 feet from the tetherball pole when the ball grazed the top of her head. Mario knows the rope that connects the tetherball to the pole is 10 feet long. He also knows that Alexis is 4 ½ feet tall. To the nearest foot, approximately how tall is the tetherball pole?
Benita created a new game that uses a triangular game board. The board is shown below. 9 in. 12 in. What is the measure of the diagonal edge? What will be the perimeter of the board? Formula: Substitute: Solve: Answer
Glenn is stretching canvas across a frame. When the canvas is stretched tight, he ll be able to paint on it. 32 in. 24 in Formula: Substitute: Solve: What is the length of the diagonal of the canvas? A: 28 in B: 40 in C: 56 in D: Not Here
There is a building with a 12 ft high window. You want to use a ladder to go up to the window, and you decide to keep the ladder 5 ft away from the building to have a good slant. How long should the ladder be? Draw Picture: Formula: Substitute: Solve:
Find the area of the largest square. 4 cm A=9 cm 2
Find the total area of all 3 squares. 8 cm A=36 cm 2
A surveyor uses the following diagram to determine the distance between two docks, A and B, on opposite sides of a lake. Which is the closest estimate of the distance between the two docks? Formula: Substitute: Solve: F 2 miles G 1 mile H 2.3 miles J 3 miles
Two birds leave the same spot at the same time. The first bird flies to his nest 11 miles south, while the other bird flies to his nest 7 miles west. How far apart are the two birds after they reach their nests? Formula: Substitute: Solve:
Lesson Quiz Use the figure for Problems 1 and 2. 1. Find the height h of the triangle. 8 m 2. Find the length of side c to the nearest meter. 12 m 10 m h c 3. An escalator in a shopping mall is 40 ft long and 32 ft tall. What distance does the escalator carry shoppers? 2624 51 ft 6 m 9 m