Angles with Correspondingly Parallel or Perpendicular Sides
Grade 7 Geometry — A New Type of Angle Relationship
📐 Introduction
We have already studied angles formed by parallel lines and a transversal — alternate interior angles, corresponding angles, and co-interior angles. Now we will explore a new type of angle relationship.
Instead of looking at angles formed by a transversal cutting parallel lines, we will compare two separate angles and ask: what happens when the sides of one angle are parallel (or perpendicular) to the sides of another angle?
🔹 Correspondingly Parallel Sides
The sides of one angle are parallel to the corresponding sides of another angle:
$OA \parallel O_1A_1$ and $OB \parallel O_1B_1$
🔸 Correspondingly Perpendicular Sides
The sides of one angle are perpendicular to the corresponding sides of another angle:
$OA \perp O_1A_1$ and $OB \perp O_1B_1$
🔍 Interactive: Explore Parallel and Perpendicular Sides
Drag the slider to see how two angles with correspondingly parallel sides relate to each other.