Question
What do you notice about the four angles created by two intersecting lines?
A. All 4 angles are congruent
B. Opposite angles are congruent (the same size and same measure)
A. All 4 angles are congruent
B. Opposite angles are congruent (the same size and same measure)
Answers
GPT-4o mini
When two lines intersect, they form four angles. The properties of these angles can be described as follows:
- **Vertical Angles**: The angles that are opposite each other (formed by the intersecting lines) are called vertical angles. Vertical angles are always congruent, meaning they have the same measure.
- **Adjacent Angles**: The angles that are next to each other (sharing a common side) are called adjacent angles. These pairs of adjacent angles are supplementary, meaning they add up to 180 degrees.
Given these observations, the correct statement about the four angles created by two intersecting lines is:
**B. Opposite angles are congruent (the same size and same measure)**.
While it is true that if the two lines are perpendicular, then all four angles would be congruent, in general, only the opposite angles (vertical angles) are guaranteed to be congruent.
- **Vertical Angles**: The angles that are opposite each other (formed by the intersecting lines) are called vertical angles. Vertical angles are always congruent, meaning they have the same measure.
- **Adjacent Angles**: The angles that are next to each other (sharing a common side) are called adjacent angles. These pairs of adjacent angles are supplementary, meaning they add up to 180 degrees.
Given these observations, the correct statement about the four angles created by two intersecting lines is:
**B. Opposite angles are congruent (the same size and same measure)**.
While it is true that if the two lines are perpendicular, then all four angles would be congruent, in general, only the opposite angles (vertical angles) are guaranteed to be congruent.