Unit 5-1 Pythagorean Triples and Dilations. Pythagorean Triples  A set of non-zero whole numbers (a, b, and c) such that a 2 + b 2 = c 2  The most common.

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Unit 5-1 Pythagorean Triples and Dilations

Pythagorean Triples  A set of non-zero whole numbers (a, b, and c) such that a 2 + b 2 = c 2  The most common Pythagorean triple is 3, 4, 5 and all multiples of 3, 4, 5 Common Pythagorean Triples 3, 4, 55, 12, 138, 15, 17 7, 24, 25 6, 8, 1010, 24, 2616, 30, 34 14, 48, 50 9, 12, 1515, 36, 3924, 45, 51 21, 72, 75 3x, 4x, 5x5x, 12x, 13x8x, 15x, 17x 7x, 24x, 25x Multiple all three numbers of the base triple by the same number, and you have another Pythagorean triple.

Pythagorean Triples Examples  Find the value of x for the following right triangles 20 x x x x

Examples using triples Damon is locked out of his house. The only open window is on the second floor, which is 12 feet above the ground. He needs to borrow a ladder from his neighbor. If he must place the ladder 5 feel from the house, to avoid the bushes, what length of ladder does Damon need? Explain your answer.

Dilation/Similar Figure Transformations  Corresponding Parts 1. Corresponding angles are equal 2. Corresponding sides are proportionate  Scale (scale factor) 1. The ratio of corresponding sides of similar shapes 2. Ratio (scale) is 3. Scale Factor is the simplified scale (reduced)  Dilation 1. Enlargement (getting bigger) 2. Reduction (getting smaller)

Units of measure and conversions

Center of dilation A B C A1A1 B1B1 C1C1 Show corresponding parts for the dilation

Graph the pre-image and its dilated image. Then, verify that the dilation is a similarity transformation. A (1, 3) B ( -1, 2) C (1, 1) (pre-image) A 1 (1, 3) B 1 (-7, -1) C 1 (1, -5) (image)

Example Jordan is putting a photo of the lacrosse team in a pull page layout in the yearbook. The original picture is 4 inches by 6 inches. If the photo in the year book is inches by inches, is the yearbook photo a dilation of the original photo? If so, what is the scale factor? Explain. Draw picture.

x A1A1 Find the coordinates for point C and write a statement of similarity y C1C1 B1B1 (0, 8) B C A (0, 4) (0, 6) (?, ?)

Determine if the dilation from A to B is an enlargement or reduction. Then find the scales of the corresponding sides, and the scale factor for the dilation. A B

Example The dimensions of a regulation tennis court are 27 feet by 78 feet. The dimensions of a ping-pong table are cm by 274 cm. Is a ping-pong table a dilation of a tennis court? Draw picture