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Find the perimeter given that AD = 4√10 units.  Simplify your answer as much as possible.

Find the perimeter given that AD = 4√10 units.  Simplify your answer as much as possible.

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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Find the perimeter given that AD = 4√10 units.  Simplify your answer as much as possible.

The image depicts a combination of geometric shapes, specifically two right-angled triangles, arranged in a connected formation. Below is a detailed explanation of the diagram: 1. **Labels and Angles:** - The vertices of the shapes are labeled as points A, B, C, and D. - The diagram contains multiple 45-degree angles. 2. **Right-Angled Triangles:** - The diagram shows two right-angled triangles stacked in such a way that the right angle (90 degrees) of one triangle (∠ABD) aligns adjacent to the right angle (∠BDC) of the second triangle. - The hypotenuses of both triangles share a common line, extending from point A through point D and ultimately intersecting with point C. 3. **Triangles and Vertices Configuration:** - In the first triangle (ΔABD), point A is at the top left, B is at the top right, and D is at the intersection where both triangles meet. - In the second triangle (ΔBDC), point B is the top left, D is at the bottom, and C forms the extended line to the right. 4. **Angles:** - ∠BAD = 45°, ∠ABD = 90°, and ∠ADB = 45° (in ΔABD). - ∠BCD = 45°, ∠BDC = 90°, and ∠BDC = 45° (in ΔBDC). 5. **Relationship between Triangles:** - Both triangles (ΔABD and ΔBDC) appear to be isosceles right triangles because they each have two 45-degree angles and one 90-degree angle which indicates the two legs are of equal length. This configuration could be used in an educational context to explain properties of right-angled and isosceles triangles, the sum of angles in a triangle, or geometric proof concepts. The visual highlights the symmetry and consistent angle properties within the connected structure.
Transcribed Image Text:The image depicts a combination of geometric shapes, specifically two right-angled triangles, arranged in a connected formation. Below is a detailed explanation of the diagram: 1. **Labels and Angles:** - The vertices of the shapes are labeled as points A, B, C, and D. - The diagram contains multiple 45-degree angles. 2. **Right-Angled Triangles:** - The diagram shows two right-angled triangles stacked in such a way that the right angle (90 degrees) of one triangle (∠ABD) aligns adjacent to the right angle (∠BDC) of the second triangle. - The hypotenuses of both triangles share a common line, extending from point A through point D and ultimately intersecting with point C. 3. **Triangles and Vertices Configuration:** - In the first triangle (ΔABD), point A is at the top left, B is at the top right, and D is at the intersection where both triangles meet. - In the second triangle (ΔBDC), point B is the top left, D is at the bottom, and C forms the extended line to the right. 4. **Angles:** - ∠BAD = 45°, ∠ABD = 90°, and ∠ADB = 45° (in ΔABD). - ∠BCD = 45°, ∠BDC = 90°, and ∠BDC = 45° (in ΔBDC). 5. **Relationship between Triangles:** - Both triangles (ΔABD and ΔBDC) appear to be isosceles right triangles because they each have two 45-degree angles and one 90-degree angle which indicates the two legs are of equal length. This configuration could be used in an educational context to explain properties of right-angled and isosceles triangles, the sum of angles in a triangle, or geometric proof concepts. The visual highlights the symmetry and consistent angle properties within the connected structure.
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