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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. Show that(a)AP Qis an equilateral triangle;(b)4AP B+4 ADQ= : Euclidean a triangle with a right angle atC.

YIU: Euclidean Geometry 7 Exercise 1. The midpoint of a chord of length 2a is at a distance d from the midpoint of the minor arc it cuts out from the circle. Show that the diameter of the circle is a 2+d d. d a a a d a b a b d B A P Q 2. Two parallel chords of a circle has lengths 168 and 72, and are at a distance 64 apart. Find the radius of ...

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