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Draw a large acute-angled triangle ABC. Carefully add the altitudes AE and BF to your drawing. Measure the lengths of AE, BF, BC, and AC. Where have you seen the equation (AE)(BC) = (BF)(AC) before? What can you say about the right triangles AEC and BFC? Justify your response.

Draw a large acute-angled triangle ABC. Carefully add the altitudes AE and BF to your drawing. Measure the lengths of AE, BF, BC, and AC. Where have you seen the equation (AE)(BC) = (BF)(AC) before? What can you say about the right triangles AEC and BFC? Justify your response.

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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**Title: Exploring Geometric Relationships in Triangles** **Instructions:** 1. **Draw Triangle ABC**: Begin by sketching a large, acute-angled triangle labeled ABC. 2. **Add Altitudes**: Carefully draw the altitudes from points A and B, labeling them as AE and BF. 3. **Measure Lengths**: Measure the lengths of segments AE, BF, BC, and AC in your drawing. 4. **Equation Analysis**: Observe the equation (AE)(BC) = (BF)(AC). Reflect on where this equation might appear in geometry. 5. **Justification**: Consider the properties of the triangles AEC and BFC. Provide a justification for the relationship indicated by the equation based on your measurements and observations. This exercise aims to deepen your understanding of geometric relationships and encourage you to explore how these concepts are interconnected.
Transcribed Image Text:**Title: Exploring Geometric Relationships in Triangles** **Instructions:** 1. **Draw Triangle ABC**: Begin by sketching a large, acute-angled triangle labeled ABC. 2. **Add Altitudes**: Carefully draw the altitudes from points A and B, labeling them as AE and BF. 3. **Measure Lengths**: Measure the lengths of segments AE, BF, BC, and AC in your drawing. 4. **Equation Analysis**: Observe the equation (AE)(BC) = (BF)(AC). Reflect on where this equation might appear in geometry. 5. **Justification**: Consider the properties of the triangles AEC and BFC. Provide a justification for the relationship indicated by the equation based on your measurements and observations. This exercise aims to deepen your understanding of geometric relationships and encourage you to explore how these concepts are interconnected.
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