Question: User: Unit 02 Honors - Reasoning and Proofs Geometry Honors Progress Monitoring Tool Preparing for MA912.C1.1 In the diagram below, AB, DE, and FC intersect at point G and \(\angle ACE\) is a right angle. Which of the following statements can be assumed from the diagram? Select all that apply. A. \(\angle AGF\) and \(\angle CGD\) are vertical angles. B. \(\angle BGD\) is a right angle. C. \(\angle AGF\) and \(\angle CGD\) are a linear pair. D. \(\angle BGE\) and \(\angle CGD\) are vertical angles. E. \(\angle AGC\) and \(\angle FGD\) are supplementary angles. F. \(\angle BGC\) and \(\angle CGD\) are complementary angles. G. FC bisects \(\angle BGD\). Preparing for MA912.C1.1 In the answer choice below, decide if each statement is an example of the Symmetric Property of Equality, the Reflexive Property of Equality, or the Transitive Property of Equality. Statements Statement #1: "AB = AB" is an example of the Statement #2: If AB = CD and CD = EF, then AB = EF is an example of the Statement #3: "WX = YZ" then "YZ = WX" is an example of the Answer A. Symmetric Property of Equality B. Reflexive Property of Equality C. Transitive Property of Equality Graph shape at top-left: a diagram of three intersecting lines with labeled points A, B, C, D, E, F, G around the intersection at G; position_hint: top-left.

1. **Problem 1: Identify which angle statements are true given the diagram with lines AB, DE, FC intersecting at G and \(\angle ACE\) a right angle.\n\n2. **Key definitions:**\n- Vertical angles are opposite angles formed by two intersecting lines and are congruent.\n- Linear pairs are adjacent angles whose non-common sides form a straight line (sum to 180\degree).\n- Supplementary angles sum to 180\degree.\n- Complementary angles sum to 90\degree.\n- A bisector divides an angle into two equal parts.\n\n3. **Analyze each statement:**\n\nA. \(\angle AGF\) and \(\angle CGD\) are vertical angles because they are opposite angles formed by intersecting lines at G. **True**.\n\nB. \(\angle BGD\) is a right angle. Since \(\angle ACE\) is right and lines intersect at G, but no direct info says \(\angle BGD\) is right. **Cannot assume true**.\n\nC. \(\angle AGF\) and \(\angle CGD\) are a linear pair. Vertical angles are not adjacent, so they cannot be a linear pair. **False**.\n\nD. \(\angle BGE\) and \(\angle CGD\) are vertical angles. They are opposite angles formed by intersecting lines at G. **True**.\n\nE. \(\angle AGC\) and \(\angle FGD\) are supplementary angles. They are adjacent and form a straight line, so sum to 180\degree. **True**.\n\nF. \(\angle BGC\) and \(\angle CGD\) are complementary angles. No info supports their sum is 90\degree. **False**.\n\nG. FC bisects \(\angle BGD\). No info given that FC divides \(\angle BGD\) into two equal parts. **Cannot assume true**.\n\n**Answer for Problem 1:** A, D, E.\n\n---\n\n1. **Problem 2: Identify the property of equality for each statement:**\n\n2. **Properties:**\n- Reflexive Property: \(a = a\)\n- Symmetric Property: If \(a = b\), then \(b = a\)\n- Transitive Property: If \(a = b\) and \(b = c\), then \(a = c\)\n\n3. **Analyze each statement:**\n\nStatement #1: "AB = AB" is Reflexive Property.\n\nStatement #2: If AB = CD and CD = EF, then AB = EF is Transitive Property.\n\nStatement #3: "WX = YZ" then "YZ = WX" is Symmetric Property.\n\n**Answer for Problem 2:**\n1: Reflexive Property (B)\n2: Transitive Property (C)\n3: Symmetric Property (A)