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Triangle ABC is a right triangle and CD 1 AB. Assume CA = a, CB = b, AD =x, DB = y, and AB = c =x+y. Use this diagram to prove the Pythagorean Theorem. a y 'B D

Triangle ABC is a right triangle and CD 1 AB. Assume CA = a, CB = b, AD =x, DB = y, and AB = c =x+y. Use this diagram to prove the Pythagorean Theorem. a y 'B D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Einstein’s Proof Triangle ABC is a right triangle and CD is perpendicular to AB. Assume \( CA = a \), \( CB = b \), \( AD = x \), \( DB = y \), and \( AB = c = x + y \). Use this diagram to prove the Pythagorean Theorem. **Diagram Explanation:** - The diagram shows triangle ABC with a right angle at C. - Line CD is perpendicular to line AB, creating two smaller right triangles, ACD and BCD. - BC is labeled as \( b \) and AC as \( a \). AB, the hypotenuse of triangle ABC, is labeled as \( c \), which is the sum of \( x \) and \( y \). - The segments AD and DB along line AB are labeled \( x \) and \( y \) respectively.
Transcribed Image Text:2. Einstein’s Proof Triangle ABC is a right triangle and CD is perpendicular to AB. Assume \( CA = a \), \( CB = b \), \( AD = x \), \( DB = y \), and \( AB = c = x + y \). Use this diagram to prove the Pythagorean Theorem. **Diagram Explanation:** - The diagram shows triangle ABC with a right angle at C. - Line CD is perpendicular to line AB, creating two smaller right triangles, ACD and BCD. - BC is labeled as \( b \) and AC as \( a \). AB, the hypotenuse of triangle ABC, is labeled as \( c \), which is the sum of \( x \) and \( y \). - The segments AD and DB along line AB are labeled \( x \) and \( y \) respectively.
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