YC and YE are opposite rays
The Correct Answer and Explanation is:
Correct Answer: True
Explanation:
In geometry, opposite rays are defined as two rays that:
- Share a common endpoint, and
- Extend in exactly opposite directions, forming a straight line.
Let’s analyze the statement: “YC and YE are opposite rays.”
For YC and YE to be opposite rays, the following must be true:
- Point Y must be the common endpoint of both rays.
- Point C must lie on one side of Y, and point E must lie on the exact opposite side such that points C, Y, and E are collinear (lie on the same line), and Y is between C and E (or at one end).
So, ray YC begins at Y and goes through point C, while ray YE begins at the same point Y and goes through point E in the opposite direction.
This situation creates a straight line with rays extending in opposite directions from a common point (Y). Therefore, rays YC and YE satisfy both conditions of opposite rays.
Visualization:
If you visualize it on a line:
mathematicaCopy EditC ----- Y ----- E
- Ray YC goes from Y towards C.
- Ray YE goes from Y towards E.
Since both rays share a common endpoint (Y) and go in exactly opposite directions on a straight line, they are considered opposite rays.
Why This Matters:
Understanding opposite rays helps in identifying linear pairs and straight angles in geometry. If two rays are opposite, the angle formed between them is 180 degrees, a key concept in proofs and geometric reasoning. Recognizing opposite rays also helps in determining relationships between points, lines, and angles in geometric figures.
Thus, the statement “YC and YE are opposite rays” is true if they share the same endpoint and lie on the same straight line extending in opposite directions.
