PPT-Pythagorean Theorem proof from similar right triangles

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. Facilitator: David Brown . May 3, 2014. Workshop Goals. Setting the stage: . Standards for Mathematical Practices. Hands-on exploration of Pythagorean triples incorporating NYS Secondary CCLS-M. Discuss geometry and algebra connections. Use the difference of two squares theorem to write the answers to the following equation.. . w = 14. 2. Answer:. ±√14. Lesson 97:. Angles and Triangles, Pythagorean Theorem, Pythagorean Triples. 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?. Theorem. A . tool. for . right . triangle. problems. What is a right triangle?. It is a triangle which has an angle that is . 90. degrees. . The two sides that make up the right angle are called . 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. for hypotenuses, legs . and distance. Pythagorean Theorem. Right Triangles. Leg. . Leg. Hypotenuse. Pythagorean Theorem. a. b. c. In a RIGHT triangle, if a and b are the lengths of the legs and c is hypotenuse, then….. 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. 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 . 2. B. 2 . = C. 2. THE PYTHAGOREAN THEOREM. LEG A. LEG B. HYPOTENUSE. PARTS OF A RIGHT TRIANGLE. THE PYTHAGOREAN THEOREM. DIAGONALS. SIDES. PARTS OF A RECTANGLE. OR SQUARE. SIDES. NOTICE TWO RIGHT TRIANGLES FORM A RECTANGLE. 1. 0. In addition to level 3.0 and beyond what was taught in class, the student may. : . Make connection with other concepts in math.. Make connection with other content areas.. Explain the relationship between the Pythagorean Theorem and the distance formula.. 4. 3. 2. 1. 0. In addition to level 3.0 and beyond what was taught in class, the student may. : . Make connection with other concepts in math.. Make connection with other content areas.. Explain the relationship between the Pythagorean Theorem and the distance formula.. Warm Up. Solve each proportion.. 1.. . . 2.. . 3.. 4. . If . ∆. QRS . ~ . ∆. XYZ. , identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides.. .