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Given EFGH is a square, GJ Match each segment or angle to its measure. E H 15 G i=15 i = 30 = 45° = 90° = 15, EF = 15/2, and LEFH = 45° =15√2 EH :: FJ :: EG HEF AGEF

Given EFGH is a square, GJ Match each segment or angle to its measure. E H 15 G i=15 i = 30 = 45° = 90° = 15, EF = 15/2, and LEFH = 45° =15√2 EH :: FJ :: EG HEF AGEF

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
ChapterCSR: Contents Of Student Resources
Section: Chapter Questions
Problem 1.39EP
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### Geometric Analysis: Square Properties and Angles **Given:** - \( EFGH \) is a square. - \( GJ = 15 \) - \( EF = 15\sqrt{2} \) - \( \angle EFH = 45^\circ \) **Problem Statement:** Match each segment or angle to its measure. **Diagram:** The given diagram depicts a square \( EFGH \) with a diagonal \( EG \). There is also an internal point \( J \) on the diagonal \( EG \). Segment \( GJ \) is marked as 15. **Tasks:** You need to match the following measures with the correct segment or angle: 1. 15 2. 30 3. 45° 4. 90° 5. \( 15\sqrt{2} \) **Segments and Angles to Match:** 1. \( \overline{EH} \) 2. \( \overline{FJ} \) 3. \( \overline{EG} \) 4. \( \angle HEF \) 5. \( \angle GEF \) **Detailed Explanation of the Diagram:** - **EH:** This is a side of the square \( EFGH \). - **FJ:** A segment from point \( F \) to an internal point \( J \). - **EG:** Diagonal of the square \( EFGH \). - **\angle HEF:** An angle at vertex \( E \) between sides \( EH \) and \( EF \). - **\angle GEF:** An angle at vertex \( E \) between sides \( GE \) and \( EF \). **Solution Approach:** 1. **\( \overline{EH} = 15 \)**: Since \( EH \) is a side of the square and \( EFG \) is a square with \( EF = EH \), and also \( EH = GJ = 15 \). 2. **\( \overline{FJ} = 15 \)**: This was marked on the diagram. 3. **\( \overline{EG} = 15\sqrt{2} \)**: This is the diagonal of square \( EFGH \). In any square, the diagonal (using Pythagoras theorem) is \( \sqrt{2} \) times the side length. 4
Transcribed Image Text:### Geometric Analysis: Square Properties and Angles **Given:** - \( EFGH \) is a square. - \( GJ = 15 \) - \( EF = 15\sqrt{2} \) - \( \angle EFH = 45^\circ \) **Problem Statement:** Match each segment or angle to its measure. **Diagram:** The given diagram depicts a square \( EFGH \) with a diagonal \( EG \). There is also an internal point \( J \) on the diagonal \( EG \). Segment \( GJ \) is marked as 15. **Tasks:** You need to match the following measures with the correct segment or angle: 1. 15 2. 30 3. 45° 4. 90° 5. \( 15\sqrt{2} \) **Segments and Angles to Match:** 1. \( \overline{EH} \) 2. \( \overline{FJ} \) 3. \( \overline{EG} \) 4. \( \angle HEF \) 5. \( \angle GEF \) **Detailed Explanation of the Diagram:** - **EH:** This is a side of the square \( EFGH \). - **FJ:** A segment from point \( F \) to an internal point \( J \). - **EG:** Diagonal of the square \( EFGH \). - **\angle HEF:** An angle at vertex \( E \) between sides \( EH \) and \( EF \). - **\angle GEF:** An angle at vertex \( E \) between sides \( GE \) and \( EF \). **Solution Approach:** 1. **\( \overline{EH} = 15 \)**: Since \( EH \) is a side of the square and \( EFG \) is a square with \( EF = EH \), and also \( EH = GJ = 15 \). 2. **\( \overline{FJ} = 15 \)**: This was marked on the diagram. 3. **\( \overline{EG} = 15\sqrt{2} \)**: This is the diagonal of square \( EFGH \). In any square, the diagonal (using Pythagoras theorem) is \( \sqrt{2} \) times the side length. 4
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