Determine whether each statement is true or false.
A chord that contains the center of the sphere is a diameter of the sphere.
A tangent of a sphere is a line that intersects a sphere in exactly two points.
true
false
draw them !!!!
A chord that contains the center of the sphere is a diameter of the sphere.
A tangent of a sphere is a line that intersects a sphere in exactly two points.
A tangent of a sphere is a line that intersects a sphere in exactly two points.
To determine whether each statement is true or false, let's understand the definitions of a chord, a diameter, a tangent, and how they relate to a sphere.
1. A chord that contains the center of the sphere is a diameter of the sphere:
To verify this statement, we need to recall the definition of a chord and a diameter:
- A chord is a line segment that connects two points on a circle.
- A diameter is a chord that passes through the center of the circle or, in this case, the center of the sphere.
To determine if this statement is true or false, we need to check if a chord that passes through the center of the sphere can be considered a diameter. The answer is true. By definition, any chord that includes the center of a sphere is a diameter of that sphere. Therefore, the statement is true.
2. A tangent of a sphere is a line that intersects a sphere in exactly two points:
To verify this statement, we need to recall the definition of a tangent:
- A tangent is a line that touches a circle or a sphere at just one point, without crossing through the object.
If a line intersects a sphere in exactly two points, it cannot be considered a tangent. Therefore, the statement is false. A tangent intersects a sphere in only one point, while a line passing through two distinct points on the sphere is called a secant, not a tangent.
In summary:
- Statement 1: True. A chord that contains the center of the sphere is a diameter of the sphere.
- Statement 2: False. A tangent of a sphere is a line that intersects a sphere at exactly one point, rather than two points.