‘Draw and label a pair of opposite rays FG and FH’
The Correct Answer and Explanation is:
Correct Answer:
To draw and label a pair of opposite rays FG and FH:
- Draw a straight line.
- Choose a point F anywhere on the line. This is the endpoint of both rays.
- Pick a point G on one side of point F, and draw a ray starting at F and going through G.
- Pick a point H on the exact opposite side of F and draw another ray starting at F and going through H.
Label the figure so that:
- Ray FG starts at F and passes through G
- Ray FH starts at F and passes through H
Explanation
In geometry, a ray is a part of a line that starts at one point and extends infinitely in one direction. The first letter in the ray’s name is always the endpoint. For example, in ray FG, point F is the endpoint, and the ray extends through point G.
Opposite rays are two rays that share the same endpoint and extend in exactly opposite directions along a straight line. They form a straight angle, which measures 180 degrees. Although they start at the same point, they do not overlap beyond that point.
To create a visual representation of opposite rays FG and FH, begin by drawing a straight line. Place a point F somewhere on the line. Then, choose two additional points: one on each side of F. Let one be G and the other be H. Draw one ray from F through G, and another ray from F through H. Since these two rays go in opposite directions and share the same endpoint F, they are called opposite rays.
This concept is useful in geometry because it helps define straight angles and understand linear pairs of angles. Opposite rays do not overlap except at their common endpoint. This property helps distinguish opposite rays from regular rays that may just share a point but not form a straight line.
By clearly drawing and labeling rays FG and FH, the relationship becomes easy to see. Such a drawing supports understanding of how rays work in geometric constructions and proofs.
