C. D Given: Circle C with inscribed quadrilateral DEFG Prove: mLD + mZF =180°, mZE + mLG = 180° ww ww

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter6: Circles
Section6.3: Line And Segment Relationships In The Circle
Problem 39E: The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle...
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E
C
G
Given: Circle C with inscribed quadrilateral DEFG
Prove: mLD + mLF =180°, mLE + mZG = 180°
%3D
wwww ww
By the arc addition postulate, the MEFG
= 360° and MFGD 4 MDEF =
360°. Using the
Theorem, the
MEDG
= 2MZF, the
MEFG
= 2mZD, the
%3D
MDEF
= 2MZG, and the MFGD = 2MZG, and the MFGD = 2mE. By the I
%3D
Substitution Property, 2mD +
= 360°, so
. Similarly,
Transcribed Image Text:E C G Given: Circle C with inscribed quadrilateral DEFG Prove: mLD + mLF =180°, mLE + mZG = 180° %3D wwww ww By the arc addition postulate, the MEFG = 360° and MFGD 4 MDEF = 360°. Using the Theorem, the MEDG = 2MZF, the MEFG = 2mZD, the %3D MDEF = 2MZG, and the MFGD = 2MZG, and the MFGD = 2mE. By the I %3D Substitution Property, 2mD + = 360°, so . Similarly,
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