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In the diagram below, ABCD is isosceles with CD CB AC. Find mLA. 40 D. A C

In the diagram below, ABCD is isosceles with CD CB AC. Find mLA. 40 D. A C

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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I need help with question number 6
**Geometry Assessment Explanation** **Problem 5:** - Given expressions for sides of a triangle: - \( A = 3(18) + 5 = 59 \) - \( B = 4(18) - 2 = 70 \) - \( C = 2(18) + 15 = 51 \) - Conclusion: \( AB \) is the shortest side. **Problem 6:** - Given an isosceles triangle \( ABCD \) where \( CD \cong CB \cong AC \). - Find \( m\angle A \). - **Diagram Explanation:** - A triangle formed by points A, B, C, D. - Line \( CD \) is parallel and equal to lines \( CB \) and \( AC \). - Angle at point A is denoted as \( x \). - An angle at point D is labeled as 40 degrees. **Problem 7 (Partial):** - In the diagram of \( \triangle ABC \), side \( BC \) is extended to point \( D \). - Angles are given as: - \( m\angle A = 3x + 2 \) - \( m\angle B = 4x \) - \( m\angle D = x + 19 \) - Find \( m\angle B \). - **Diagram Explanation:** - The triangle \( \triangle ABC \) with an extended line to point \( D \). - Markings on angles as described above. For students, it is crucial to understand the properties of isosceles triangles and how to determine unknown angles using provided angle expressions.
Transcribed Image Text:**Geometry Assessment Explanation** **Problem 5:** - Given expressions for sides of a triangle: - \( A = 3(18) + 5 = 59 \) - \( B = 4(18) - 2 = 70 \) - \( C = 2(18) + 15 = 51 \) - Conclusion: \( AB \) is the shortest side. **Problem 6:** - Given an isosceles triangle \( ABCD \) where \( CD \cong CB \cong AC \). - Find \( m\angle A \). - **Diagram Explanation:** - A triangle formed by points A, B, C, D. - Line \( CD \) is parallel and equal to lines \( CB \) and \( AC \). - Angle at point A is denoted as \( x \). - An angle at point D is labeled as 40 degrees. **Problem 7 (Partial):** - In the diagram of \( \triangle ABC \), side \( BC \) is extended to point \( D \). - Angles are given as: - \( m\angle A = 3x + 2 \) - \( m\angle B = 4x \) - \( m\angle D = x + 19 \) - Find \( m\angle B \). - **Diagram Explanation:** - The triangle \( \triangle ABC \) with an extended line to point \( D \). - Markings on angles as described above. For students, it is crucial to understand the properties of isosceles triangles and how to determine unknown angles using provided angle expressions.
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