1. **Problem Statement:** Determine whether the given angle name statements are True (T) or False (F) based on the figure with points A-H on a horizontal line and points J-M on a diagonal line intersecting at D. 2. **Understanding Angle Naming:** An angle is named by three points where the middle point is the vertex. For example, \(\angle MDC\) has vertex at \(D\) and rays \(DM\) and \(DC\). 3. **Check each statement:** - 1. \(\angle MDC\) and \(\angle MDB\) name the same angle? - \(\angle MDC\) has points M-D-C. - \(\angle MDB\) has points M-D-B. - Since points C and B are different and on opposite sides of D, these are different angles. - **Answer: F** - 2. \(\angle KDE\) and \(\angle FDJ\) name the same angle? - \(\angle KDE\) has points K-D-E. - \(\angle FDJ\) has points F-D-J. - Points K and F are different, E and J are different, so these are different angles. - **Answer: F** - 3. \(\angle MDC\) is an acute angle? - The diagonal line \(JM\) intersects horizontal line \(ABCD...\) at D. - \(\angle MDC\) is formed between diagonal \(DM\) and horizontal \(DC\). - This angle is less than 90 degrees. - **Answer: T** - 4. \(\angle KDE\) is an obtuse angle? - \(\angle KDE\) is between \(DK\) (diagonal) and \(DE\) (horizontal). - This angle is greater than 90 degrees. - **Answer: T** - 5. \(\angle LDE\) and \(\angle MDE\) name the same angle? - \(\angle LDE\) is L-D-E. - \(\angle MDE\) is M-D-E. - Points L and M are different, so these are different angles. - **Answer: F** - 6. \(\angle KDE\) is an acute angle? - From step 4, \(\angle KDE\) is obtuse. - **Answer: F** **Final answers:** 1. F 2. F 3. T 4. T 5. F 6. F