Complete the explanation, which proves the Chord-Chord Product Theorem. Glven: Chords AB and CD Intersect at point E. Prove: AE EB = CE ED (Hint: Draw AC and BD.) D. v, then AC and BD can be drawn. Since through any two points there (select) ZACD (select) v because they intercept the same arc. ZCEA (select) v by the Vertical Angles Theorem. Therefore, AAEC and (select) v are similar by the AA Similarity Theorem. Corresponding СЕ AE sides are proportional, so ED (select) v CE AE (EB ED)= ED · (EB ED), or AE EB = (select) v (select) v

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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Complete the exxplanation, which proves the Chord-Chord Product Theorem.
Glven: Chords AB and CD Intersect at point E.
Prove: AE EB = CE ED (Hint: Draw AC and BD)
D.
vthen AC and BD can be drawn.
Since through any two points there (select)
LACD (select) v because they intercept the same arc. ZCEA (select) vby the Vertical Angles
Theorem. Therefore, AAEC and (select) v are similar by the AA Similarity Theorem. Corresponding
CE
AE
sides are proportional, so
ED
(select) v
CE
AE
- (EB ED)=
ED
(EB ED), or AE EB (select) v
(select) v
Transcribed Image Text:Question Example Step by Step tint Complete the exxplanation, which proves the Chord-Chord Product Theorem. Glven: Chords AB and CD Intersect at point E. Prove: AE EB = CE ED (Hint: Draw AC and BD) D. vthen AC and BD can be drawn. Since through any two points there (select) LACD (select) v because they intercept the same arc. ZCEA (select) vby the Vertical Angles Theorem. Therefore, AAEC and (select) v are similar by the AA Similarity Theorem. Corresponding CE AE sides are proportional, so ED (select) v CE AE - (EB ED)= ED (EB ED), or AE EB (select) v (select) v
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