Assignment P : 1-17, even, 28-31, Challenge Problems

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 quickly find a missing side length in a right triangle

Tangram Activity Take out your 7 tangrams, or if you don’t have them, cut out some new ones. Step 1: In the center of a new sheet of paper, trace one of the large right triangles.

Tangram Activity Step 2: Use all of your tangram pieces to assemble two squares along the legs of your traced triangle so that the length of each leg is equal to the side length of the square. Trace all of the pieces.

Tangram Activity Step 3: Find the area of each assembled square. How does your answer relate to the length of each leg?

Tangram Activity Step 4: Use all of your tangram pieces to assemble a square along the hypotenuse of your traced triangle so that the side length of the square is equal to the length of the hypotenuse. Trace all of the pieces.

Tangram Activity Step 5: Find the area of the large square. How does your answer relate to the length of the hypotenuse?

Tangram Activity Step 6: How do the areas of each square relate to each other? How do the areas of the squares relate the legs and hypotenuse of your traced triangle?

Investigation 1 Use the Geometer’s Sketchpad Activity to investigate the relationship between the legs of a right triangle and its hypotenuse. Click on the picture to start.

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? √375

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

Example 5 What is the area of the large square?

Example 6 Find the area of the triangle. h = 4 A=1/2bh A=20

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. x7=28 x7=35 21=7x

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? Draw a picture

Assignment P : 1-17, even, 28-31, Challenge Problems