My geometry teacher said something about when putting supplementary down for the answer doesn't quite necessarily work all the time. Is that true? Why is that? Would it be best just to put linear pair in for supplementary?
Yes, it is true that putting "supplementary" as the answer doesn't always work in geometry. Let's explore why and when "linear pair" may be a better choice.
In geometry, when two angles add up to 180 degrees, they are called supplementary angles. But simply stating that the angles are supplementary might not be sufficient to prove a specific relationship or solve a problem.
Reasons why "supplementary" may not always work as the answer:
1. Lack of context: Without additional information, simply knowing that two angles are supplementary doesn't provide any specific details about their placement or properties.
2. Other angle relationships: There are many other angle relationships in geometry that are not classified as supplementary. For example, angles may be complementary (adding up to 90 degrees) or congruent (having the same measure), among others.
3. Angle measurement restrictions: Certain geometric situations may have angle measurements that prevent them from being supplementary. For instance, in a triangle, the three interior angles must add up to 180 degrees, which means they cannot all be supplementary to each other.
On the other hand, if you have a pair of adjacent angles that form a straight line, they are called a linear pair. Linear pairs are always supplementary, meaning they add up to 180 degrees. However, not all supplementary angles form linear pairs.
To determine if "supplementary" or "linear pair" is the appropriate term to use, consider the given information and the problem context. If two angles are known to form a straight line, calling them a linear pair is more appropriate. If the relationship between two angles is not specified or can be described by any supplementary pair, then "supplementary" is a more general term to use.
Overall, it's important to understand the specific properties and context of angles in geometry to choose the most accurate and relevant description for your answer.