Transcription of Pythagoras Theorem and Its Applications
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Pythagoras Theorem and Its Applications
Chapter 1 Pythagoras Theoremand Its Pythagoras Theorem and its Pythagoras TheoremThe lengthsa b<cof the sides of a right triangle satisfy the relationa2+b2= Converse TheoremIf the lengths of the sides of a triangles satisfy the relationa2+b2=c2,thenthe triangle contains a right : Euclidean a triangle withBC=a,CA=b,andAB=csatisfy-inga2+b2=c2 . Consider another triangleXY ZwithYZ=a, XZ=b,6 XZY=90 .By the Pythagorean Theorem ,XY2=a2+b2=c2,sothatXY= the triangles4 ABC 4XY Zby the SSS test. This means that6 ACB=6 XZYis a right Dissect two given squares into triangles and quadrilaterals and re-arrange the pieces into a equilateral triangles inside a linesAXandAYare extended to intersectBCandCDrespec-tively atPandQ.
4. ABPQ is a rectangle constructed on the hypotenuse of a right trian-gle ABC. X and Y are the intersections of AB with CP and CQ respectively. 3Answer: The distance from the center to the longer chord is 13. From this, the radius of the circle is 85. More generally, if these chords has lengths 2a and 2b,andthedistance
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