lesson 6-6
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Lesson 6-6. The Pythagorean Theorem. 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:. - PowerPoint PPT PresentationTRANSCRIPT
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