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E В F A An 8 in. by 8 in. square air vent is shown where AG = 8 %3D inches. BFis the midsegment of AADG and C'Eis the midsegment of ADBF. Which of the following is measure of CE? 2 inches 3 inches 4 inches 6 inches

E В F A An 8 in. by 8 in. square air vent is shown where AG = 8 %3D inches. BFis the midsegment of AADG and C'Eis the midsegment of ADBF. Which of the following is measure of CE? 2 inches 3 inches 4 inches 6 inches

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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### Square Air Vent Geometry Problem #### Diagram Description: The image shows a square air vent with multiple nested squares forming a pyramid-like structure. There is a triangle AGD inscribed within the square with points B, C, E, and F marked on the sides and within the triangle. - **Point A** is at the bottom left of the square. - **Point G** is at the bottom right of the square. - **Point D** is at the top (center of the nested squares). Points B, C, E, and F are defined as follows: - **Point B** is along the segment AG, halfway from A. - **Point C** is along AD, halfway from A. - **Point E** is along DG, halfway from D. - **Point F** is along segment AG, halfway from G. #### Problem Statement: An 8 in. by 8 in. square air vent is shown where \( AG = 8 \) inches. \( \overline{BF} \) is the midsegment of \( \triangle ADG \) and \( \overline{CE} \) is the midsegment of \( \triangle DBF \). Which of the following is the measure of \( \overline{CE} \)? #### Answer Options: - \( \quad \) 2 inches - \( \quad \) 3 inches - \( \quad \) 4 inches - \( \quad \) 6 inches
Transcribed Image Text:### Square Air Vent Geometry Problem #### Diagram Description: The image shows a square air vent with multiple nested squares forming a pyramid-like structure. There is a triangle AGD inscribed within the square with points B, C, E, and F marked on the sides and within the triangle. - **Point A** is at the bottom left of the square. - **Point G** is at the bottom right of the square. - **Point D** is at the top (center of the nested squares). Points B, C, E, and F are defined as follows: - **Point B** is along the segment AG, halfway from A. - **Point C** is along AD, halfway from A. - **Point E** is along DG, halfway from D. - **Point F** is along segment AG, halfway from G. #### Problem Statement: An 8 in. by 8 in. square air vent is shown where \( AG = 8 \) inches. \( \overline{BF} \) is the midsegment of \( \triangle ADG \) and \( \overline{CE} \) is the midsegment of \( \triangle DBF \). Which of the following is the measure of \( \overline{CE} \)? #### Answer Options: - \( \quad \) 2 inches - \( \quad \) 3 inches - \( \quad \) 4 inches - \( \quad \) 6 inches
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