is this inverse statement true or false
if 2 angles are a linear pair of angles they are adjacent
True.
False
The inverse statement should be
if 2 angles are not a linear pair of angles then they are not adjacent
Yes, you are correct. The inverse statement of "If 2 angles are a linear pair of angles, they are adjacent" would be "If 2 angles are not a linear pair of angles, they are not adjacent."
To determine whether the inverse statement is true or false, we need to understand what an inverse statement is.
The inverse of a conditional statement switches the hypothesis and conclusion of the original statement, and also negates both. In this case, the original statement is: "If two angles are a linear pair of angles, then they are adjacent."
To find the inverse statement, we switch the hypothesis and conclusion, and negate both parts: "If two angles are not a linear pair of angles, then they are not adjacent."
Now, let's consider the given inverse statement: "If two angles are a linear pair of angles, they are adjacent."
This statement is false. In fact, the original statement ("If two angles are a linear pair of angles, then they are adjacent") is true, but its inverse statement is false.
To determine this, you can think of two angles that are not adjacent but are still a linear pair. For example, consider a straight line, and two angles that are not adjacent but together form a line, such as a 90-degree angle and a 270-degree angle. These angles are a linear pair but are not adjacent. Thus, the inverse statement is false.