Prove the following result, needed to demonstrate the Saccheri- Legendre theorem (see Figure 4.27). Let D be the midpoint of BC and E the unique point on AD such that A D E and AD = DE. Then AAEC has the same angle sum as AABC, and either (

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
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Prove the following result, needed to demonstrate the Saccheri-
Legendre theorem (see Figure 4.27). Let D be the midpoint of BC
and E the unique point on AD such that A D E and AD = DE.
Then AAEC has the same angle sum as AABC, and either (EAC)°
or (KAEC)° is S} (*BAC). (Hint: First show that ABDA = ACDE,
then that (EAC) + (XAEC)° = (*BAC).)
B.
RE 4.27 A
Transcribed Image Text:Prove the following result, needed to demonstrate the Saccheri- Legendre theorem (see Figure 4.27). Let D be the midpoint of BC and E the unique point on AD such that A D E and AD = DE. Then AAEC has the same angle sum as AABC, and either (EAC)° or (KAEC)° is S} (*BAC). (Hint: First show that ABDA = ACDE, then that (EAC) + (XAEC)° = (*BAC).) B. RE 4.27 A
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