Defining Vertical Angles
Defining Vertical Angles is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings, where students learn that vertical angles are the opposite pairs formed when two lines intersect, that they are always congruent (equal in measure), and apply this theorem to find unknown angle measures in diagrams. This is one of the most fundamental angle relationships in geometry.
Key Concepts
Vertical angles are opposite angles formed when two lines intersect. Vertical angles are always congruent (equal in measure): if $\angle 1$ and $\angle 3$ are vertical angles, then $\angle 1 = \angle 3$.
Common Questions
What are vertical angles?
Vertical angles are the two pairs of opposite angles formed when two lines intersect. They share the same vertex but not a common side. Vertical angles are always congruent (have the same measure).
Why are vertical angles always equal?
Both angles in a vertical pair are supplementary to the same adjacent angle, so they must each equal 180 degrees minus that adjacent angle, making them equal to each other.
How do you use vertical angles to find missing angle measures?
If two lines intersect and one angle is labeled, its vertical angle across the intersection is equal. The two adjacent angles are supplementary (sum to 180 degrees).
What is Big Ideas Math Advanced 2 Chapter 12 about?
Chapter 12 covers Constructions and Scale Drawings, including geometric constructions, properties of quadrilaterals, angle relationships (vertical angles, complementary, supplementary), and scale drawings.