Congruent supplements theorem
The Congruent Supplements Theorem, also known as the Vertical Angles Theorem, states that if two angles are vertical angles (opposite each other when two lines intersect), then they are congruent
The Congruent Supplements Theorem, also known as the Vertical Angles Theorem, states that if two angles are vertical angles (opposite each other when two lines intersect), then they are congruent.
To understand the Congruent Supplements Theorem, let’s consider a diagram:
\ |\
\ | \
\ | \
\|\ \
————-
\ | /
\ | /
\|/
In the given diagram, two lines intersect each other, creating four angles at the intersection point. These angles are labeled as ∠1, ∠2, ∠3, and ∠4.
The theorem states that if ∠1 and ∠2 are vertical angles (opposite each other when the lines intersect), then ∠1 and ∠2 are congruent.
Similarly, if ∠3 and ∠4 are vertical angles, then ∠3 and ∠4 are congruent.
The reason behind this theorem is that vertical angles are formed by the same pair of intersecting lines, so their measurements are equal.
Mathematically, we can express this as:
If ∠1 and ∠2 are vertical angles, then ∠1 ≅ ∠2.
If ∠3 and ∠4 are vertical angles, then ∠3 ≅ ∠4.
Note that the word “congruent” (symbol ≅) represents that the angles have the same measure or size.
You can use this theorem to solve various geometric problems involving intersecting lines, such as finding missing angle measures or proving geometric statements. It is a useful tool in geometry to establish relationships between angles formed by intersecting lines.
More Answers:
Understanding the Converse in Mathematics: Swapping the Hypothesis and ConclusionUnderstanding the Vertical Angles Theorem: Explained and Illustrated
Understanding the Congruent Complements Theorem: Explaining the Relationship Between Complementary and Congruent Angles