Adjacent Angles
Adjacent angles are a Grade 7 geometry concept in Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings, where adjacent angles share both a common vertex and a common side without overlapping interiors. For example, angle AOB and angle BOC are adjacent if they share vertex O and side OB. Adjacent angles are fundamental for understanding how angles combine to form right angles and straight angles.
Key Concepts
Adjacent angles are two angles that share a common vertex and a common side, but have no interior points in common. If angles $\angle ABC$ and $\angle CBD$ are adjacent, they share vertex $B$ and common side $\overrightarrow{BC}$.
Common Questions
What are adjacent angles?
Adjacent angles share a common vertex and exactly one common side, with no overlapping interiors. They are like two puzzle pieces that fit perfectly along one edge.
What two conditions must adjacent angles satisfy?
Adjacent angles must share the same vertex (corner point) and exactly one common side (ray). The interiors of the two angles must not overlap.
How are adjacent angles related to supplementary or complementary angles?
Adjacent angles can be complementary (summing to 90 degrees) or supplementary (summing to 180 degrees) when they form a right angle or straight angle together, but not all adjacent angles have these special sums.
What textbook covers adjacent angles in Grade 7?
Big Ideas Math Advanced 2, Chapter 12: Constructions and Scale Drawings introduces adjacent angles as a foundational angle relationship concept.