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In the following sketch, AF|| BE. Prove that ACDF is a cyclic quadrilateral.

In the following sketch, AF|| BE. Prove that ACDF is a cyclic quadrilateral.

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.
Chapter4: Quadrilaterals
Section4.3: The Rectangle, Square, And Rhombus
Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...
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Please help me with this question by using one or more of these three methods in picture 1.
Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. X>D B Br • +X = 180° Quadrilateral ABCD with B+Ô=180° Given: Conclusion: ABCD is a cyclic quad 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. Quadrilateral ABCD with BC extended to E. BÂD=EĈD. Reason: Given: Conclusion: ABCD is a cyclic quad 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: Four points A, B, C and D with A and D on the same side of BC. BẬC=BIC Conclusion: ABCD is a cyclic quad Reason: line subtends = Z 53 -- ---- ---
Transcribed Image Text:Theorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of these If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. X>D B Br • +X = 180° Quadrilateral ABCD with B+Ô=180° Given: Conclusion: ABCD is a cyclic quad 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. Quadrilateral ABCD with BC extended to E. BÂD=EĈD. Reason: Given: Conclusion: ABCD is a cyclic quad 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: Four points A, B, C and D with A and D on the same side of BC. BẬC=BIC Conclusion: ABCD is a cyclic quad Reason: line subtends = Z 53 -- ---- ---
In the following sketch, AF || BE. Prove that ACDF is a cyclic quadrilateral. (e) F Statement Reason LA +L Bi = 180 DeWot CorAspanding Ls BE I| AF Lf+LEI = 180° 1orrespandings BEl AE
Transcribed Image Text:In the following sketch, AF || BE. Prove that ACDF is a cyclic quadrilateral. (e) F Statement Reason LA +L Bi = 180 DeWot CorAspanding Ls BE I| AF Lf+LEI = 180° 1orrespandings BEl AE
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