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11 Consider a regular tetrahedron ABCD of edge a. I is the midpoint of [BC] and [AH] is a height in triangle ADI. a) Prove that (AH) is perpendicular to the plane (ВCD). b) Calculate the angle between the two planes (АВС) and (BCD). c) Calculate the angle between (AD) and the plane (BCD). 1RCDEFGH

11 Consider a regular tetrahedron ABCD of edge a. I is the midpoint of [BC] and [AH] is a height in triangle ADI. a) Prove that (AH) is perpendicular to the plane (ВCD). b) Calculate the angle between the two planes (АВС) and (BCD). c) Calculate the angle between (AD) and the plane (BCD). 1RCDEFGH

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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Consider a regular tetrahedron ABCD of edge a. I is the midpoint of [BC] and [AH] is a height in triangle ADI. a) Prove that (AH) is perpendicular to the plane (ВCD). b) Calculate the angle between the two planes (АВС) and (BCD). c) Calculate the angle between (AD) and the plane (BCD). uhe 4BCDEFGH.
Transcribed Image Text:Consider a regular tetrahedron ABCD of edge a. I is the midpoint of [BC] and [AH] is a height in triangle ADI. a) Prove that (AH) is perpendicular to the plane (ВCD). b) Calculate the angle between the two planes (АВС) and (BCD). c) Calculate the angle between (AD) and the plane (BCD). uhe 4BCDEFGH.
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