Lesson 6-6Lesson 6-6

The Pythagorean The Pythagorean TheoremTheorem

Ohio Content Standards:

Ohio Content Standards:

Find the square root of perfect squares, and approximate the square root of

non-perfect squares.

Ohio Content Standards:

Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies;

e.g., (square root of 130) is between 11 and 12.

Ohio Content Standards:

Estimate, compute and solve problems involving scientific notation, square roots

and numbers with integer exponents.

Ohio Content Standards:

Apply order of operations to simplify expressions and perform computations

involving integer exponents and radicals.

Ohio Content Standards:

Estimate the solutions for problem situations involving square and cube roots.

Ohio Content Standards:

Establish the validity of conjectures about geometric objects, their properties and

relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards:Make, test and establish the validity of conjectures about

geometric properties and relationships using counterexample, inductive and deductive reasoning, and

paragraph or two-column proof, including:a. prove the Pythagorean Theorem;

b. prove theorems involving triangle similarity and congruence;

c. prove theorems involving properties of lines, angles, triangles and quadrilaterals;

d. test a conjecture using basic constructions made with a compass and straightedge or technology.

Ohio Content Standards:

Use right triangle trigonometric relationships to determine lengths and

angle measures.

Ohio Content Standards:

Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle

measures in similar figures.

Pythagorean Theorem

Pythagorean TheoremIn a right triangle, the square of the

lengths of the hypotenuse c is equal to the sum of the squares of the lengths

of the legs a and b.

Pythagorean TheoremIn a right triangle, the square of the

lengths of the hypotenuse c is equal to the sum of the squares of the lengths

of the legs a and b.

aa22 ++ b b22 = = cc22

Pythagorean Theorem

a

aa22 + + bb22 = = cc22

b

c

Find the length of the Find the length of the hypotenuse of the right hypotenuse of the right

triangle.triangle.

16 ft

12 ft

Find the length of one leg of a Find the length of one leg of a right triangle if the length of the right triangle if the length of the hypotenuse is 4 meters and the hypotenuse is 4 meters and the

length of the other leg is 3 length of the other leg is 3 meters.meters.

3 m4 m

If If cc is the measure of the is the measure of the hypotenuse, find the missing hypotenuse, find the missing

measure. Round to the nearest measure. Round to the nearest tenth, if necessary.tenth, if necessary.

a a = ?, = ?, b b = 10, = 10, cc = 20 = 20

The lengths of the three sides of a The lengths of the three sides of a triangle are 4, 5, and 6 meters. triangle are 4, 5, and 6 meters.

Determine whether this triangle is Determine whether this triangle is a right triangle.a right triangle.

Assignment:Assignment:

Pg. 260 Pg. 260 18-36 evens18-36 evens