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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.

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.

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.
Chapter3: Triangles
Section3.1: Congruent Triangles
Problem 6E: In a right triangle, the sides that form the right angle are the legs; the longest side opposite the...
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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 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 ---- B トーー • +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. B --- E Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Reason: Given: ext Z of quad = opp int Z Conclusion: ABCD is a cyclic quad 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. Four points A, B, C and D with A and D on the same side of BC. BẬC= BIC Reason: line subtends = Zs Given: Conclusion: ABCD is a cyclic quad 53 ト、。 トーー
Transcribed Image Text: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 ---- B トーー • +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. B --- E Quadrilateral ABCD with BC extended to E. BẬD = EĈD. Reason: Given: ext Z of quad = opp int Z Conclusion: ABCD is a cyclic quad 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. Four points A, B, C and D with A and D on the same side of BC. BẬC= BIC Reason: line subtends = Zs Given: Conclusion: ABCD is a cyclic quad 53 ト、。 トーー
In the following sketch, DC is a common tangent to both circles at C and AD is a tangent to the larger circle at A. Prove that ABCD is a cyclic quadrilateral. Reason Statement
Transcribed Image Text:In the following sketch, DC is a common tangent to both circles at C and AD is a tangent to the larger circle at A. Prove that ABCD is a cyclic quadrilateral. Reason Statement
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