Please help me with this question by using these three theorems in picture 1. (e)In the following sketch, AF || BE. Provethat ACDF is a cyclic quadrilateral.(g)FStatementReason TO PROVE THAT A QUADRILATERAL IS CYCLICTheorems 4 to 6 were about the properties of a cyclic quadrilateral. The converses of thesetheorems are used to prove that a given quadrilateral is cyclic.If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.CONVERSE OF THEOREM 4Br•+X = 180°Quadrilateral ABCD with ÊB+D=180°Given:Conclusion: ABCD is a cyclic quadReason:opp Zs of quad supplCONVERSE OF THEOREM 5If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral iscyclic.DBEEQuadrilateral ABCD with BC extended to E. BÂD=EĈD.Reason:Given:Conclusion: ABCD is a cyclic quadext Z of quad = opp int 2CONVERSE OF THEOREM 6If a line segment joining two points subtends equal angles at two points on the same side of the linesegment, then the four points are concyclic.BBFour points A, B, C and D with A and D on the same side of BC. BẬC=BI CReason:Given:line subtends = ZsConclusion: ABCD is a cyclic quad53---

Using of the given theorem we prove ACDF is cyclic quadrilateral

Answered: In the following sketch, AF|| BE. Prove…

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

Elementary Geometry For College Students, 7e

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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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Question

Please help me with this question by using these three theorems in picture 1.

(e)
In the following sketch, AF || BE. Prove
that ACDF is a cyclic quadrilateral.
(g)
F
Statement
Reason

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.
If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.
CONVERSE OF THEOREM 4
Br
•+X = 180°
Quadrilateral ABCD with ÊB+D=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.
D
B
E
E
Quadrilateral ABCD with BC extended to E. BÂD=EĈD.
Reason:
Given:
Conclusion: ABCD is a cyclic quad
ext Z of quad = opp int 2
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
B
Four points A, B, C and D with A and D on the same side of BC. BẬC=BI C
Reason:
Given:
line subtends = Zs
Conclusion: ABCD is a cyclic quad
53
---

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