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Check it out! - PPT Presentation

1 173 Proving the Pythagorean Theorem Using Similarity Woodworkers must accurately cut and assemble each piece of wood to ensure that a project is square Every vertical piece should intersect every horizontal piece at a 90 angle To ID: 444857

pythagorean length square theorem length pythagorean theorem square proving similarity congruent 212 door measured 198 lengths woodworker calculate project

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Slide1

Check it out!

1

1.7.3: Proving the Pythagorean Theorem Using SimilaritySlide2

Woodworkers must accurately cut and assemble each piece of wood to ensure that a project

is “

square.” Every vertical piece should intersect every horizontal piece at a 90˚ angle. To

determine if

a project is square, woodworkers use the Pythagorean Theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the longest side. If the lengths of the diagonals are equal, then the project is square.

2

1.7.3: Proving the Pythagorean Theorem Using SimilaritySlide3

A woodworker measured the

length

of one diagonal of the

wooden

door, , to be 212 cm. The

woodworker measured the

length of to be 198 cm

and the length of to be 76 cm. Calculate the length of .Is congruent to ?Is the door “square”? Explain your answer.

3

1.7.3: Proving the Pythagorean Theorem Using Similarity

198 cm

76 cmSlide4

A woodworker measured the length of one diagonal of the wooden door, , to be 212 cm. The woodworker measured the length of to be 198 cm and the length of to be 76 cm. Calculate the length of

.

and are the two shorter sides ofUse the Pythagorean Theorem to calculate the length of .

4

1.7.3: Proving the Pythagorean Theorem Using SimilaritySlide5

The

length

of

is

cm, or approximately 212.1 cm.51.7.3: Proving the Pythagorean Theorem Using Similarity

Pythagorean Theorem

Substitute values for

a

and b.Simplify.Take the positive square root of both sides.39,204 + 5776 = c2

44,980 =

c

2

a2

+ b2 = c

2

(198)2

+

(76)2 = c

2Slide6

Is congruent to

?The length of

was measured to be 212 cm.The calculated length of is , or approximately 212.1 cm.Although the lengths are close, they are not congruent.

6

1.7.3: Proving the Pythagorean Theorem Using SimilaritySlide7

Is the door “square”? Explain your answer

.To be square, the lengths of each diagonal must be congruent.

The lengths are not congruent; therefore, the door, as assembled, is not square.

7

1.7.3: Proving the Pythagorean Theorem Using Similarity