PPT-Pythagorean Theorem proof from similar right triangles

Author : min-jolicoeur | Published Date : 2015-09-27

A geometric realization of a proof in H Wus Teaching Geometry According to the Common Core Standards B A C c a b Given a right triangle ABC with legs a and

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Pythagorean Theorem proof from similar right triangles: Transcript

A geometric realization of a proof in H Wus Teaching Geometry According to the Common Core Standards B A C c a b Given a right triangle ABC with legs a and b and hypotenuse . Written by: Jack S. . Calcut. Presented by: Ben Woodford. (pay attention: there Will be a test at the end). Definitions. An . angle is . rational . provided it is commensurable with a straight . angle; equivalently. Theorem. A . tool. for . right . triangle. problems . only. When do I need to use. the Pythagorean Theorem ?. When I know: length of 2 sides. And. Need to know: length of 3rd side. What is the Pythagorean Theorem?. Strategies to differentiate instruction. (secondary). Jacque Melin. melinj@gvsu.edu. www.formativedifferentiated.com. Thank you for being present today. You can expect:. conversations. learning. I’m counting on you to…. Pythagorean theorem converse. .. practice. Tell whether the given triangle is a right triangle.. 1. 2. . More theorems. .. Theorem practice. Tell whether the segments with the given side lengths can form a triangle. If so, classify the triangle as . Drawings 1 - 2. #1. Perpendicular to a line. #2. Skew lines and transversal. Drawings 3 - 4. #3. Parallel lines and transversal. #4. Marking congruent angles. Drawings 5 - 6. #5. Acute angles. #6. Obtuse angles. Nicole Scicutella. Goals. Students will develop an understanding of the pythagorean theorem using jelly beans. Students will have a visual understanding of area reflects on pythagorean theorem. OBJECTIVES. The Pythagorean Theorem. In words:. As an equation:. Pythagorean Triples. A set of nonzero whole numbers a, b, and c that satisfy the equation . is called a Pythagorean triple. Example: 3, 4, 5 or 8, 15, 17. for grades 9-12. Erica Papa. Table of Contents . Title Page. Table of contents. Where did the Pythagorean Theorem come from? . Pythagoras. Pythagorean Theorem equation. Can you label the triangle?. Leading to Pythagorean Triples. .. . OR. . . a. 2. b. 2. = c. 2. c. a. b. leg. leg. hypotenuse. Pythagorean Triples. A set of nonzero whole numbers a, b, and c that satisfy the equation a. 2. b. 2. = c. 2. Here are some common ones to remember:. Using Congruent Triangles. Congruent triangles have congruent corresponding parts. So, if you can prove the two triangles are congruent then you know their corresponding parts must be congruent as well.. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Geometry. Pythagorean Theorem. Warm Up. Classify each triangle by its angle measures.. 1.. . . 2.. . 3. . Simplify . 4. . If . Robert “Dr. Bob” Gardner. Based on Hungerford’s . Appendix to Section V.3 . in . Algebra. , Springer-. Verlag. (1974). The field of complex numbers, . , is algebraically closed.. . Lemma . V.3.17. Pythagorean Theorem Review. The Pythagorean Theorem states:. . in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. . a. 2. b. 2. = c. Proportions and Similar Figures What is Similarity? Not Similar Similar Similar Not Similar Similar Triangles Similar Figures Figures that have the same shape but not necessarily the same size are

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