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Let AABC be the spherical triangle shown in Figure 4.3. Perform the construction in the proof of Theorem 4.1.2 on the sphere, starting with this triangle. Convince yourself that the point F constructed is in the interior of LACD if and only if u(LBAC) < 90°. Draw diagrams illustrating both possibilities.

Let AABC be the spherical triangle shown in Figure 4.3. Perform the construction in the proof of Theorem 4.1.2 on the sphere, starting with this triangle. Convince yourself that the point F constructed is in the interior of LACD if and only if u(LBAC) < 90°. Draw diagrams illustrating both possibilities.

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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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2. Let AABC be the spherical triangle shown in Figure 4.3. Perform the construction in the proof of Theorem 4.1.2 on the sphere, starting with this triangle. Convince yourself that the point F constructed is in the interior of LACD if and only if u(LBAC) < 90°. Draw diagrams illustrating both possibilities. B FIGURE 4.3: A spherical triangle Theorem 4.1.2 (Exterior Angle Theorem). The measure of an exterion is strictly greater than the measure of either remote interior angle.
Transcribed Image Text:2. Let AABC be the spherical triangle shown in Figure 4.3. Perform the construction in the proof of Theorem 4.1.2 on the sphere, starting with this triangle. Convince yourself that the point F constructed is in the interior of LACD if and only if u(LBAC) < 90°. Draw diagrams illustrating both possibilities. B FIGURE 4.3: A spherical triangle Theorem 4.1.2 (Exterior Angle Theorem). The measure of an exterion is strictly greater than the measure of either remote interior angle.
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