# Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the...

date post

29-Dec-2015Category

## Documents

view

225download

2

Embed Size (px)

### Transcript of Pythagorean Theorem 5.4. Learn the Pythagorean Theorem. Define Pythagorean triple. Learn the...

Pythagorean Theorem 5.4

Learn the Pythagorean Theorem.Define Pythagorean triple.Learn the Pythagorean Inequality.Solve problems with the Pythagorean Theorem and Inequality.

The Pythagorean Theorem is probably the most famous mathematical relationship. It states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.a2 + b2 = c2

Find the value of x. Give your answer in simplest radical form.a2 + b2 = c2Pythagorean Theorem22 + 62 = x2Substitute 2 for a, 6 for b, and x for c.40 = x2Simplify.Find the positive square root.Simplify the radical.

Find the value of x. Give your answer in simplest radical form.a2 + b2 = c2Pythagorean Theorem42 + 82 = x2Substitute 4 for a, 8 for b, and x for c.80 = x2Simplify.Find the positive square root.Simplify the radical.

A set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2 is called a Pythagorean triple.

Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.The side lengths are nonzero whole numbers that satisfy the equation a2 + b2 = c2, so they form a Pythagorean triple.a2 + b2 = c2Pythagorean Theorem142 + 482 = c2Substitute 14 for a and 48 for b.2500 = c2Multiply and add.50 = cFind the positive square root.

Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.a2 + b2 = c2Pythagorean Theorem82 + 102 = c2164 = c2

Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.The side lengths are nonzero whole numbers that satisfy the equation a2 + b2 = c2, so they form a Pythagorean triple.a2 + b2 = c2Pythagorean Theorem242 + b2 = 262Substitute 24 for a and 26 for c.b2 = 100Multiply and subtract.b = 10Find the positive square root.

Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.No. The side length 2.4 is not a whole number.

The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths.

You can also use side lengths to classify a triangle as acute or obtuse.

To understand why the Pythagorean inequalities are true, consider ABC.

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.5, 7, 10Since 2< 10 < 12; 5, 7, and 10 can be the side lengths of a triangle.Classify the triangle.Since c2 > a2 + b2, the triangle is obtuse.Add and compare.100 > 74Multiply.Compare c2 to a2 + b2.Substitute the longest side for c.

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.Determine if the measures form a triangle. 5, 8, 17

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.7, 12, 16Since 5 < 16 < 19; 7, 12, and 16 can be the side lengths of a triangle.Classify the triangle.Since c2 > a2 + b2, the triangle is obtuse.Add and compare.256 > 193Multiply.Compare c2 to a2 + b2.Substitute the longest side for c.

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.Determine if the measures form a triangle. 11, 18, 34

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.3.8, 4.1, 5.2Since .3< 5.2 < 7.9; 3.8, 4.1, and 5.2 can be the side lengths of a triangle.Classify the triangle.Since c2 < a2 + b2, the triangle is acute.Add and compare.27.04 < 31.25Multiply.Compare c2 to a2 + b2.Substitute the longest side for c.

Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

13; yes; the side lengths are nonzero whole numbers that satisfy Pythagoreans Theorem.

Tell if the measures 7, 11, and 15 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.

yes; obtuse

Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.a.b.Yes a triangle can be formed 1 < 6 < 9AcuteYes a triangle can be formed 16 < 26 < 36Rightc.Yes a triangle can be formed 5 < 25 < 35Right

Find the exact answer of the missing side.a.b.c.d.e.f.

a.b.c.x = 25x = 34d.e.f.Find the exact answer of the missing side.

a.b.c.x = 15x = 51d.e.f.x = 60x = 30Find the exact answer of the missing side.

a.b.c.x = 15x = 51d.e.f.Find the exact answer of the missing side.x = 82

Assignment

Section 5.4 8 - 30

*