Math 8 Unit 1: Square Roots and the Pythagorean Theorem

What you’ll learn: Determine the square of a number Determine the square root of a number Determine the approximate square root of a non-perfect square Develop and apply the Pythagorean Theorem

Unit 1: Square Roots and the Pythagorean Theorem Why it’s important Used in construction to ensure 90 0 corners Used in surveying Used to determine the distance between two locations (video games)

1.1 SQUARE NUMBERS AND AREA MODELS Unit 1: Square Roots and the Pythagorean Theorem

1.1 Square Numbers and Area Models Focus: Relate the area of a square and square numbers

1.1 Square Numbers and Area Models On a piece of grid paper draw as many different rectangles as you can with an area of: 4 squares 6 squares 8 squares 9 squares

1.1 Square Numbers and Area Models What are the differences and similarities between squares and rectangles? Differences Rectangle sides have length and width Square has all four sides the same Similarities Quadrilaterals, parallelograms: 4 sides 90 o (right) corners Parallel sides

1.1 Square Numbers and Area Models Use grid paper to draw several different squares. How does the side length relate to the area?

1.1 Square Numbers and Area Models What are the square numbers from 0 to 100?

1.1 Square Numbers and Area Models What is the equation for the perimeter of a square? S S S S

1.1 Square Numbers and Area Models Homework

1.2 SQUARES AND SQUARE ROOTS Unit 1: Square Roots and the Pythagorean Theorem

1.2 Squares and Square Roots Focus: Find the squares and square roots of whole numbers

1.2 Squares and Square Roots What numbers have only two factors? What are these numbers called? Which numbers have an even number of factors, but more than 2 factors? Which numbers have an odd number of factors? What are these numbers called?

1.2 Squares and Square Roots Remember division: dividend divisor quotient

1.2 Squares and Square Roots Draw a square with an area of 36 squares. What is the side length?

1.2 Squares and Square Roots The square root of a number is when the divisor and quotient of a number are the same. The square root is the opposite of the square.

1.2 Squares and Square Roots Homework

1.3 MEASURING LINE SEGMENTS Unit 1: Square Roots and the Pythagorean Theorem

1.3 Measuring Line Segments Focus: Use the area of a square to find the length of a line segment

1.3 Measuring Line Segments Do the investigate questions

1.3 Measuring Line Segments Try example 1

1.3 Measuring Line Segments Try example 2

1.3 Measuring Line Segments Not all numbers have whole number square roots. If it doesn’t have a whole number root than leave the number as a root.

1.3 Measuring Line Segments Homework

1.4 ESTIMATING SQUARE ROOTS Unit 1: Square Roots and the Pythagorean Theorem

1.4 Estimating Square Roots Focus: Develop strategies for estimating a square root.

1.4 Estimating Square Roots Investigate Estimate the square roots of 2, 5, 11, 18, and 24

1.4 Estimating Square Roots Homework

1.5 THE PYTHAGOREAN THEOREM Unit 1: Square Roots and the Pythagorean Theorem

1.5 The Pythagorean Theorem Focus: Discover a relationship among the side lengths of a right triangle

1.5 The Pythagorean Theorem Draw a right angle with legs 3 cm and 4 cm long. Measure the length of the diagonal. Draw a right angle with legs 12 cm and 5 cm long. Measure the length of the diagonal. Draw a right angle with legs 12 cm and 16 cm long. Measure the length of the diagonal 5 cm 13 cm 20 cm

1.5 The Pythagorean Theorem Right angle triangle Right angle Hypotenuse (diagonal, opposite the right angle, longest side)

1.5 The Pythagorean Theorem Pythagorean Theorem a b c a and b are legs and c must be the hypotenuse

Pythagorean triples Whole number triples that satisfy the Pythagorean theorem. – 3, 4, 5 – 5, 12, 13 – 7, 24, 25 – 8, 15, 17 – 9, 40, 41

1.5 The Pythagorean Theorem Example What is the length of the hypotenuse of a triangle with legs 6 cm and 10 cm? a = 6 cm b = 10cm c

1.5 The Pythagorean Theorem Homework

1.6 EXPLORING THE PYTHAGOREAN THEOREM Unit 1: Square Roots and the Pythagorean Theorem

1.6 Exploring the Pythagorean Theorem Focus: Use the Pythagorean Theorem to identify right triangle

1.6 Exploring the Pythagorean Theorem There are many different types of triangles. (some overlap) Right Triangle – has a 90 o angle Isosceles Triangle – two sides are the same length and two angles are the same Obtuse Triangle – one internal angle is obtuse (>90 o ) Acute Triangle – all angles are less than 90 o Scalene Triangle – all three sides are different lengths

1.6 Exploring the Pythagorean Theorem Length of Shortest Side Area of Square on Shortest Side Length of Second Side Area of Square on Second Side Length of Longest Side Area of Square on Longest Side Obtuse Triangle Acute Triangle Investigate Work in a group of 4 with four different triangles

1.6 Exploring the Pythagorean Theorem Homework

1.7 APPLYING THE PYTHAGOREAN THEOREM Unit 1: Square Roots and the Pythagorean Theorem

1.7 Applying the Pythagorean Theorem Focus: Solve problems using the Pythagorean Theorem

1.7 Applying the Pythagorean Theorem Example An antenna has a height of 10 m. The anchor for the guy wire is 8 m from the base. How long should the guy wire be? 10 m 8 m antenna-witch-can-mount-on-the-roof-of-the-building/

1.7 Applying the Pythagorean Theorem a = 10 m b = 8 m 10 m 8 m The guy wire is m long.

1.7 Applying the Pythagorean Theorem Example A father is building a slide for his children. The slide is 3 m long and the slide will be mounted to a platform 1.5 m above the ground. How far away horizontally will the slide end? e-Slide-Large.jpg 1.5 m3 m

1.7 Applying the Pythagorean Theorem c = 3 m a = 1.5 m b = ? 3 m 1.5 m

1.7 Applying the Pythagorean Theorem Homework