In the following sketch, EFG is a tangent to circle BFC at F. Prove that ABCD is a cyclic quadrilateral. If B =x, express the following (1) (2) in terms of x. Give reasons: (i) 21 (ii) (iii) Ê+Ê, E G. Statement

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
Section4.1: Properties Of A Parallelogram
Problem 24E: In quadrilateral ABCD, the midpoints of opposite sides are joined to form two intersecting segments....
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Please help me with this question by using these three theorems in picture 1. It is not graded it is just numbers 1) and 2)
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
If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.
CONVERSE OF THEOREM 4
E
son
B
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
Tfan exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is
сyclic.
Br
- --
Given:
Quadrilateral ABCD with BC extended to E. BÂD=EĈD.
Conclusion: ABCD is a cyclic quad
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
Four points A, B, C and D with A and D on the same side of BC. BẬC=B.C
Reason:
Given:
Conclusion: ABCD is a cyclic quad
line subtends = Zs
53
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 If the opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic. CONVERSE OF THEOREM 4 E son B 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 Tfan exterior angle of a quadrilateral is equal to the opposite interior angle then the quadrilateral is сyclic. Br - -- Given: Quadrilateral ABCD with BC extended to E. BÂD=EĈD. Conclusion: ABCD is a cyclic quad 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 Four points A, B, C and D with A and D on the same side of BC. BẬC=B.C Reason: Given: Conclusion: ABCD is a cyclic quad line subtends = Zs 53
(h)
In the following sketch, EFG is a tangent
to circle BFC at F.
TO 1
(1)
Prove that ABCD is a cyclic
quadrilateral.
If B, = x, express the following
The
(2)
CO
in terms of x. Give reasons:
If a
(i)
tang
(ii)
(iii)
E
Statement
Reason
Giv
Com
CO
If a
Transcribed Image Text:(h) In the following sketch, EFG is a tangent to circle BFC at F. TO 1 (1) Prove that ABCD is a cyclic quadrilateral. If B, = x, express the following The (2) CO in terms of x. Give reasons: If a (i) tang (ii) (iii) E Statement Reason Giv Com CO If a
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