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TO PROVE THAT A QUADRILATERAL IS CYCLIC Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these theorems are used to prove that a given quadrilateral is cyclic. CONVERSE OF THEOREM 4 If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. D Br •+X = 180° Quadrilateral ABCD with B+D=180° Given: Conclusion: ABCD is a cyclic quad %3D Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is cyclic. B BK

TO PROVE THAT A QUADRILATERAL IS CYCLIC Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these theorems are used to prove that a given quadrilateral is cyclic. CONVERSE OF THEOREM 4 If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. D Br •+X = 180° Quadrilateral ABCD with B+D=180° Given: Conclusion: ABCD is a cyclic quad %3D Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is cyclic. B BK

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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Please help me with this question by using one or more of these three methods in picture 1.
TO PROVE THAT A QUADRILATERAL IS CYCLIC theorems are used to prove that a given quadrilateral is cyclic. Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these CONVERSE OF THEOREM 4 osite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. BK • +X = 180° Given: Conclusion: ABCD is a cyclic quad Quadrilateral ABCD with B+Ô=180° Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is cyclic. B Br --- E Given: Conclusion: ABCD is a cyclic quad Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Reason: ext Z of quad = opp int Z CONVERSE OF THEOREM 6 If a line segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic. B Given: Conclusion: ABCD is a cyclic quad Four points A, B, C and D with A and D on the same side of BC. BÂC=BÔI C Reason: line subtends = Zs ---
Transcribed Image Text:TO PROVE THAT A QUADRILATERAL IS CYCLIC theorems are used to prove that a given quadrilateral is cyclic. Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these CONVERSE OF THEOREM 4 osite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. BK • +X = 180° Given: Conclusion: ABCD is a cyclic quad Quadrilateral ABCD with B+Ô=180° Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is cyclic. B Br --- E Given: Conclusion: ABCD is a cyclic quad Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Reason: ext Z of quad = opp int Z CONVERSE OF THEOREM 6 If a line segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic. B Given: Conclusion: ABCD is a cyclic quad Four points A, B, C and D with A and D on the same side of BC. BÂC=BÔI C Reason: line subtends = Zs ---
(e) In the following sketch, AF || BE. Prove that ACDF is a cyclic quadrilateral. E F Statement Reason
Transcribed Image Text:(e) In the following sketch, AF || BE. Prove that ACDF is a cyclic quadrilateral. E F Statement Reason
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