Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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**Title: Understanding Triangle Congruence: The HL Theorem** **Problem Statement:** State what additional information is required in order to know that the triangles are congruent for the reason given. **Concept:** HL (Hypotenuse-Leg) Congruence **Diagram Explanation:** The image shows a geometric diagram with two right triangles, \( \triangle WUC \) and \( \triangle VUC \), sharing a common side \( UC \). - Both \( \angle WUC \) and \( \angle VUC \) are right angles, denoted by red squares. - \( WU \) and \( VC \) are corresponding sides. **Task:** Identify the additional information needed to apply the HL Congruence Theorem. This theorem states that two right triangles are congruent if the hypotenuse and one corresponding leg are equal. **Input Fields:** - Two input fields are provided to type the necessary criteria for congruence based on the HL theorem. To apply the HL Theorem, you would need to know whether: - **Type your answer…**: The length of the hypotenuse \( WU \) is equal to the length of \( VC \) (i.e., \( WU = VC \) ). - **= Type your answer…**: The length of the leg \( UC \) is shared, therefore already known to be equal in both triangles. By establishing these equalities, you can deduce that \( \triangle WUC \equiv \triangle VUC \).
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Transcribed Image Text:**Title: Understanding Triangle Congruence: The HL Theorem** **Problem Statement:** State what additional information is required in order to know that the triangles are congruent for the reason given. **Concept:** HL (Hypotenuse-Leg) Congruence **Diagram Explanation:** The image shows a geometric diagram with two right triangles, \( \triangle WUC \) and \( \triangle VUC \), sharing a common side \( UC \). - Both \( \angle WUC \) and \( \angle VUC \) are right angles, denoted by red squares. - \( WU \) and \( VC \) are corresponding sides. **Task:** Identify the additional information needed to apply the HL Congruence Theorem. This theorem states that two right triangles are congruent if the hypotenuse and one corresponding leg are equal. **Input Fields:** - Two input fields are provided to type the necessary criteria for congruence based on the HL theorem. To apply the HL Theorem, you would need to know whether: - **Type your answer…**: The length of the hypotenuse \( WU \) is equal to the length of \( VC \) (i.e., \( WU = VC \) ). - **= Type your answer…**: The length of the leg \( UC \) is shared, therefore already known to be equal in both triangles. By establishing these equalities, you can deduce that \( \triangle WUC \equiv \triangle VUC \).
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