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If GE = 34 units, find the length of DF in Rectangle DEFG.

If GE = 34 units, find the length of DF in Rectangle DEFG.

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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If GE = 34 units, find the length of DF in Rectangle DEFG. 

### Diagram Description and Transcription In this diagram, we have a rectangle labeled \(DEFG\). 1. **Vertices and Sides:** - The rectangle has four vertices: \(D\), \(E\), \(F\), and \(G\), - Side \(DE\) is vertical on the right side with a length of \(16\) units, - Side \(FG\) is horizontal at the bottom with a length of \(30\) units. 2. **Diagonals:** - The rectangle has two diagonals: \(DF\) and \(EG\), - These diagonals intersect at point \(H\), in the center of the rectangle. ### Explanation for Educational Purpose This diagram serves to illustrate several geometric concepts related to rectangles. #### Properties of Rectangles: 1. **Opposite Sides:** Rectangles have opposite sides that are equal in length. Here, \(DE = FG = 16\) and \(DF = EG = 30\). 2. **Diagonals:** The diagonals of a rectangle are equal in length and bisect each other. In this case, diagonals \(DF\) and \(EG\) intersect at point \(H\), splitting each diagonal into two equal parts. 3. **Right Angles:** All internal angles in a rectangle are right angles (90 degrees). This property ensures that the opposite sides are parallel and equal. 4. **Intersection Point:** The point \(H\) where the diagonals intersect is the midpoint of both diagonals of the rectangle. This means that: - \(DH = HF\) - \(EH = HG\) This diagram can be used as a reference for understanding the basic properties of rectangles, particularly useful in geometry studies.
Transcribed Image Text:### Diagram Description and Transcription In this diagram, we have a rectangle labeled \(DEFG\). 1. **Vertices and Sides:** - The rectangle has four vertices: \(D\), \(E\), \(F\), and \(G\), - Side \(DE\) is vertical on the right side with a length of \(16\) units, - Side \(FG\) is horizontal at the bottom with a length of \(30\) units. 2. **Diagonals:** - The rectangle has two diagonals: \(DF\) and \(EG\), - These diagonals intersect at point \(H\), in the center of the rectangle. ### Explanation for Educational Purpose This diagram serves to illustrate several geometric concepts related to rectangles. #### Properties of Rectangles: 1. **Opposite Sides:** Rectangles have opposite sides that are equal in length. Here, \(DE = FG = 16\) and \(DF = EG = 30\). 2. **Diagonals:** The diagonals of a rectangle are equal in length and bisect each other. In this case, diagonals \(DF\) and \(EG\) intersect at point \(H\), splitting each diagonal into two equal parts. 3. **Right Angles:** All internal angles in a rectangle are right angles (90 degrees). This property ensures that the opposite sides are parallel and equal. 4. **Intersection Point:** The point \(H\) where the diagonals intersect is the midpoint of both diagonals of the rectangle. This means that: - \(DH = HF\) - \(EH = HG\) This diagram can be used as a reference for understanding the basic properties of rectangles, particularly useful in geometry studies.
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