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and ∠BAC = θ. We can trisect the side BC (do NOT prove this), say D and E are the points that trisect BC. The claim is that the angles BAD, DAE and EAC are then the trisections of θ. To show this is not true, we assume that those angles are equal and let φ, α, β, l and d be as given in the diagram.   (a)  Prove that triangles ABD and ACE are congruent. 1 (b)  Using the sine rule in triangles ABD and ADE show that α = β. 3 (c)  Use triangle ABD to explain why α ̸= β.

and ∠BAC = θ. We can trisect the side BC (do NOT prove this), say D and E are the points that trisect BC. The claim is that the angles BAD, DAE and EAC are then the trisections of θ. To show this is not true, we assume that those angles are equal and let φ, α, β, l and d be as given in the diagram.   (a)  Prove that triangles ABD and ACE are congruent. 1 (b)  Using the sine rule in triangles ABD and ADE show that α = β. 3 (c)  Use triangle ABD to explain why α ̸= β.

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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Given an angle θ, we construct an isosceles triangle ABC with AB = AC and ∠BAC = θ. We can trisect the side BC (do NOT prove this), say D and E are the points that trisect BC. The claim is that the angles BAD, DAE and EAC are then the trisections of θ. To show this is not true, we assume that those angles are equal and let φ, α, β, l and d be as given in the diagram.

 

  1. (a)  Prove that triangles ABD and ACE are congruent. 1

  2. (b)  Using the sine rule in triangles ABD and ADE show that α = β. 3

  3. (c)  Use triangle ABD to explain why α ̸= β.

d. d E d t triangles ABD and ACE are congruent. dtv
Transcribed Image Text:d. d E d t triangles ABD and ACE are congruent. dtv
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