Write a paragraph proof of the Hinge Theorem.Given: WX AB, WY AC, mZW>mZAYCProve: XY > BCWAUse the following outline.Find a point D outside AABC so AD WY and ZDAB ZYWX.• Show that AWXY AABD.• Construct the angle bisector of ZCAD. Let point E be the pointDEC.where the angle bisector intersects BD.• Show that AACE AADE so CE DE.• Show that DB = CE + EB.• Use the Triangle Inequality Theorem on ABCE.ABNow, let ELabel a point D outside AABC so that AD = WY and ZDAB = ZYWX. Since WX AB, AWXY AABD bySince AE bisects ZCAD,be the point where the angle bisector of ZCAD intersects BD. By the Reflexive Property, AE =ByThus, AACE = AADE bySince AACE E AADE, CEZCAEBecause AD = WY, AD =+ EB, and since CE DE, DB =+ EB. By applying the Triangle Inequalitythe Segment Addition Postulate, DB =and> BC. Because AWXY AABD, by CPCTC, XYTheorem to ABCE, CE + EB BC. This means thatXY > BC.%23

Answered: Image /qna-images/answer/a6d19ec4-4fb0-492c-911c-b12227686fd4.jpg

Label a point D outside AABC so that AD WY and ZDAB ZYWX. Since WX AB, AWXY AABD by Now, let E be the point where the angle bisector of ZCAD intersects BD. By the Reflexive Property, AE Since AE bisects ZCAD, ZCAE E V Because AD WY, AD = V Thus, AACE AADE by ▼ Since ΔACE스 ΔADE, CE 스 V By the Segment Addition Postulate, DB = + EB, and since CE DE, DB = + EB. By applying the Triangle Inequality Theorem to ABCE, CE + EB VBC. This means that V> BC. Because AWXY AABD, by CPCTC, XY = V and XY > BC.

Label a point D outside AABC so that AD WY and ZDAB ZYWX. Since WX AB, AWXY AABD by Now, let E be the point where the angle bisector of ZCAD intersects BD. By the Reflexive Property, AE Since AE bisects ZCAD, ZCAE E V Because AD WY, AD = V Thus, AACE AADE by ▼ Since ΔACE스 ΔADE, CE 스 V By the Segment Addition Postulate, DB = + EB, and since CE DE, DB = + EB. By applying the Triangle Inequality Theorem to ABCE, CE + EB VBC. This means that V> BC. Because AWXY AABD, by CPCTC, XY = V and XY > BC.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.2: Angles And Their Relationships

Problem 10E: Suppose that AB,AC,AD,AE, and AF are coplanar, Exercises 10-13 Classify the following as true or...

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