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В A An 8 in. by 8 in. square air vent is shown where AG 8 inches. BFIS the midsegment of AADG and CEis the midsegment of ADBF. Which of the following is measure of CE? O 2 inches O 3 inches O 4 inches

В A An 8 in. by 8 in. square air vent is shown where AG 8 inches. BFIS the midsegment of AADG and CEis the midsegment of ADBF. Which of the following is measure of CE? O 2 inches O 3 inches O 4 inches

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 38E
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**Mathematics: Midsegments in Triangles** **Problem:** Consider the diagram shown, representing an 8 inch by 8 inch square air vent. Points A, B, C, D, E, F, and G are labeled in a triangular and linear configuration. The length AG is given as 8 inches. Key points to consider: - \(BF\) is the midsegment of \(\triangle ADG\). - \(CE\) is the midsegment of \(\triangle DBF\). **Question:** What is the measure of \(CE\)? **Options:** A. 2 inches B. 3 inches C. 4 inches D. 6 inches **Solution Explanation:** - In \(\triangle ADG\), \(BF\) is the midsegment, so it is half the length of \(AG\). - Since \(AG = 8\) inches, \(BF = \frac{1}{2} \times 8 = 4\) inches. - Similarly, in \(\triangle DBF\), \(CE\) is the midsegment. Thus, \(CE\) is half the length of \(BF\). - Since \(BF = 4\) inches, \(CE = \frac{1}{2} \times 4 = 2\) inches. So, the measure of \(CE\) is 2 inches. **Correct Answer:** A. 2 inches
Transcribed Image Text:**Mathematics: Midsegments in Triangles** **Problem:** Consider the diagram shown, representing an 8 inch by 8 inch square air vent. Points A, B, C, D, E, F, and G are labeled in a triangular and linear configuration. The length AG is given as 8 inches. Key points to consider: - \(BF\) is the midsegment of \(\triangle ADG\). - \(CE\) is the midsegment of \(\triangle DBF\). **Question:** What is the measure of \(CE\)? **Options:** A. 2 inches B. 3 inches C. 4 inches D. 6 inches **Solution Explanation:** - In \(\triangle ADG\), \(BF\) is the midsegment, so it is half the length of \(AG\). - Since \(AG = 8\) inches, \(BF = \frac{1}{2} \times 8 = 4\) inches. - Similarly, in \(\triangle DBF\), \(CE\) is the midsegment. Thus, \(CE\) is half the length of \(BF\). - Since \(BF = 4\) inches, \(CE = \frac{1}{2} \times 4 = 2\) inches. So, the measure of \(CE\) is 2 inches. **Correct Answer:** A. 2 inches
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