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ram, DG || EF

ram, DG || EF

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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#### Identifying Properties of Isosceles Trapezoids In the given diagram, the coordinates for points D, E, F, and G are as follows: - D: (-2, 2) - E: (-4, -3) - F: (3, -3) - G: (1, 2) It is stated that line DG is parallel to line EF. **Objective:** Determine what additional information would prove that DEFG is an isosceles trapezoid. **Graph Explanation:** The graph shows a quadrilateral plotted on a coordinate plane. The vertices of the quadrilateral DEFG form a shape where DG is parallel to EF as indicated. Since for a trapezoid at least one pair of opposite sides must be parallel, this condition is met. To prove that DEFG is an isosceles trapezoid, we need to demonstrate that the non-parallel sides (DE and GF or DG and EF) are equal in length. **Options Given:** - DE ≅ GF - DE ≅ DG - EF ≅ DG - EF ≅ GF Choose the correct option to make DEFG an isosceles trapezoid. **Options Analysis:** - DE ≅ GF: This would make the non-parallel sides equal, which is characteristic of an isosceles trapezoid. - DE ≅ DG: This would not help in proving the quadrilateral is an isosceles trapezoid, as DG is parallel to EF. - EF ≅ DG: Both are already parallel, so this information is redundant. - EF ≅ GF: This is not a property needed to prove a trapezoid is isosceles. **Conclusion:** The correct additional information to prove that DEFG is an isosceles trapezoid is that DE ≅ GF. --- **Answer:** - **DE ≅ GF** --- **Navigation Options:** - **Mark this and return** - **Save and Exit** - **Next** - **Submit**
Transcribed Image Text:#### Identifying Properties of Isosceles Trapezoids In the given diagram, the coordinates for points D, E, F, and G are as follows: - D: (-2, 2) - E: (-4, -3) - F: (3, -3) - G: (1, 2) It is stated that line DG is parallel to line EF. **Objective:** Determine what additional information would prove that DEFG is an isosceles trapezoid. **Graph Explanation:** The graph shows a quadrilateral plotted on a coordinate plane. The vertices of the quadrilateral DEFG form a shape where DG is parallel to EF as indicated. Since for a trapezoid at least one pair of opposite sides must be parallel, this condition is met. To prove that DEFG is an isosceles trapezoid, we need to demonstrate that the non-parallel sides (DE and GF or DG and EF) are equal in length. **Options Given:** - DE ≅ GF - DE ≅ DG - EF ≅ DG - EF ≅ GF Choose the correct option to make DEFG an isosceles trapezoid. **Options Analysis:** - DE ≅ GF: This would make the non-parallel sides equal, which is characteristic of an isosceles trapezoid. - DE ≅ DG: This would not help in proving the quadrilateral is an isosceles trapezoid, as DG is parallel to EF. - EF ≅ DG: Both are already parallel, so this information is redundant. - EF ≅ GF: This is not a property needed to prove a trapezoid is isosceles. **Conclusion:** The correct additional information to prove that DEFG is an isosceles trapezoid is that DE ≅ GF. --- **Answer:** - **DE ≅ GF** --- **Navigation Options:** - **Mark this and return** - **Save and Exit** - **Next** - **Submit**
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