Example 1 1.What is the area of a square with a side length of 4 inches? x inches? 2.What is the side length of a square with an area of 25 in 2 ? x in.

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The Pythagorean Theorem and its Converse

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Example 1 1.What is the area of a square with a side length of 4 inches? x inches? 2.What is the side length of a square with an area of 25 in 2 ? x in 2 ? x x

Parts of a Right Triangle Which segment is the longest in any right triangle?

7.1 Apply the Pythagorean Theorem Objectives: 1.To discover and use the Pythagorean Theorem 2.To use Pythagorean Triples to find quickly find a missing side length in a right triangle

The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

The Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Example 2 The triangle below is definitely not a right triangle. Does the Pythagorean Theorem work on it?

Example 3 How high up on the wall will a twenty- foot ladder reach if the foot of the ladder is placed five feet from the wall?

Example 4: SAT In figure shown, what is the length of RS?

Example 5 What is the area of the large square?

Example 6 Find the area of the triangle.

Pythagorean Triples Pythagorean Triples Three whole numbers that work in the Pythagorean formulas are called Pythagorean Triples.

Example 7 What happens if you add the same length to each side of a right triangle? Do you still get another right triangle?

Example 8 What happens if you multiply all the side lengths of a right triangle by the same number? Do you get another right triangle?

Pythagorean Multiples Pythagorean Multiples Conjecture: If you multiply the lengths of all three sides of any right triangle by the same number, then the resulting triangle is a right triangle. In other words, if a 2 + b 2 = c 2, then (an) 2 + (bn) 2 = (cn) 2.

Pythagorean Triples Pythagorean Triples

Primitive Pythagorean Triples primitive Pythagorean triple A set of Pythagorean triples is considered a primitive Pythagorean triple if the numbers are relatively prime; that is, if they have no common factors other than

Example 9 Find the length of one leg of a right triangle with a hypotenuse of 35 cm and a leg of 28 cm.

Example 10 Use Pythagorean Triples to find each missing side length.

Example 11 A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down 4 feet, how many feet will the bottom slip out?