Question: Which of the angle pairs listed below actually form Linear Pairs? Please make all the necessary
selections.
A
B
C
D
E
F
A: a horizontal line with one slanted ray rising up to the right from a point on the line, position_hint \in {top-left}
B: two separate right-angle shapes, each with a vertical segment rising from a short horizontal base, position_hint \in {top-left}
C: a horizontal ray to the left and a slanted ray rising up to the right meeting at a vertex, position_hint \in {bottom-left}
D: a horizontal line with two slanted rays rising up from nearby points near the center, position_hint \in {top-right}
E: two intersecting slanted lines crossing near the center-right, position_hint \in {center}
F: a vertical line with a horizontal ray extending to the right from the middle, forming a T-shape, position_hint \in {bottom-right}
1. **Problem Statement:** Identify which angle pairs from options A, B, C, D, E, and F form linear pairs.
2. **Definition:** A linear pair consists of two adjacent angles whose non-common sides form a straight line (i.e., they are supplementary and adjacent).
3. **Analysis of each option:**
- **A:** A horizontal line with one slanted ray rising up to the right from a point on the line. This forms two adjacent angles sharing a vertex on the line, and the non-common sides form a straight line. \(\Rightarrow\) **Forms a linear pair.**
- **B:** Two separate right-angle shapes, each with a vertical segment rising from a short horizontal base. These are separate shapes, so angles are not adjacent or sharing a vertex. \(\Rightarrow\) **Does not form a linear pair.**
- **C:** A horizontal ray to the left and a slanted ray rising up to the right meeting at a vertex. The two rays meet at a vertex and the horizontal ray and slanted ray form adjacent angles, but the non-common sides do not form a straight line. \(\Rightarrow\) **Does not form a linear pair.**
- **D:** A horizontal line with two slanted rays rising up from nearby points near the center. Since the rays originate from different points, angles are not adjacent. \(\Rightarrow\) **Does not form a linear pair.**
- **E:** Two intersecting slanted lines crossing near the center-right. Intersecting lines form vertical angles, but linear pairs require adjacent angles with a straight line. Here, adjacent angles formed by intersecting lines do form linear pairs. \(\Rightarrow\) **Forms a linear pair.**
- **F:** A vertical line with a horizontal ray extending to the right from the middle, forming a T-shape. The angles adjacent to the horizontal ray and vertical line form a linear pair because the non-common sides form a straight line. \(\Rightarrow\) **Forms a linear pair.**
4. **Final selections:**
- Linear pairs are formed in options **A, E, and F**.
**Answer:** A, E, F