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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
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Write a paragraph proof of the Hinge Theorem. Given: WX AB, WY AC, mZW>mZA Y C Prove: XY > BC W A Use 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 point D E C. 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. A B Now, let E Label a point D outside AABC so that AD = WY and ZDAB = ZYWX. Since WX AB, AWXY AABD by Since AE bisects ZCAD, be the point where the angle bisector of ZCAD intersects BD. By the Reflexive Property, AE = By Thus, AACE = AADE by Since AACE E AADE, CE ZCAE Because AD = WY, AD = + EB, and since CE DE, DB = + EB. By applying the Triangle Inequality the Segment Addition Postulate, DB = and > BC. Because AWXY AABD, by CPCTC, XY Theorem to ABCE, CE + EB BC. This means that XY > BC. %23
Transcribed Image Text:Write a paragraph proof of the Hinge Theorem. Given: WX AB, WY AC, mZW>mZA Y C Prove: XY > BC W A Use 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 point D E C. 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. A B Now, let E Label a point D outside AABC so that AD = WY and ZDAB = ZYWX. Since WX AB, AWXY AABD by Since AE bisects ZCAD, be the point where the angle bisector of ZCAD intersects BD. By the Reflexive Property, AE = By Thus, AACE = AADE by Since AACE E AADE, CE ZCAE Because AD = WY, AD = + EB, and since CE DE, DB = + EB. By applying the Triangle Inequality the Segment Addition Postulate, DB = and > BC. Because AWXY AABD, by CPCTC, XY Theorem to ABCE, CE + EB BC. This means that XY > BC. %23
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