CONVERS fthe opposite angles of a quadrilateral a are supplementary, then the quadrilateral is cyclio

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.
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.
If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is
Reason
ト--ン
•+X = 180°
Quadrilateral ABCD with B+D=180°
Given:
Reason:
opp Zs of quad suppl
CONVERSE OF THEOREM 5
cyclic.
B
ト。
Given:
Quadrilateral ABCD with BC extended to E. BÂD= EĈD.
Conclusion: ABCD is a cyclic quad
Reason:
ext Z of quad = opp int 2
CONVERSE OF THEOREM 6
na 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.
D
B
Given:
Conclusion: ABCD is a cyclic quad
our points A, B, C and D with A and D on the same side of BC. BẬC=BI.C
line subtends = Zs
Reason:
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. If an exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is Reason ト--ン •+X = 180° Quadrilateral ABCD with B+D=180° Given: Reason: opp Zs of quad suppl CONVERSE OF THEOREM 5 cyclic. B ト。 Given: Quadrilateral ABCD with BC extended to E. BÂD= EĈD. Conclusion: ABCD is a cyclic quad Reason: ext Z of quad = opp int 2 CONVERSE OF THEOREM 6 na 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. D B Given: Conclusion: ABCD is a cyclic quad our points A, B, C and D with A and D on the same side of BC. BẬC=BI.C line subtends = Zs Reason: 53 ---
(h)
In the following sketch, EFG is a tangent
to circle BFC at F.
(1)
TO P
Prove that ABCD is a cyclic
quadrilateral.
The c
(2)
If B, = x, express the following
in terms of x. Give reasons:
CON
(i)
(ii)
If a
(iii)
Ê+Ê,
tang
E
Statement
G.
Reason
(i)
In the fol
Transcribed Image Text:(h) In the following sketch, EFG is a tangent to circle BFC at F. (1) TO P Prove that ABCD is a cyclic quadrilateral. The c (2) If B, = x, express the following in terms of x. Give reasons: CON (i) (ii) If a (iii) Ê+Ê, tang E Statement G. Reason (i) In the fol
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