Geometry
Basics of Congruence
In the last topic, we covered the fundamentals of Angles, Lines, and Shapes. Now, let’s talk about how congruence plays a role in geometry.
Here’s the process that we’ll be using to solve these types of equations:
When lines intersect, the intersections form angles with unique relationships. We will use these angle relationships to explain how to construct parallel or perpendicular lines, which help us to bisect angles and line segments. Parallel sides will also be used to reveal the properties of parallelograms.
Congruent Shapes: If one shape can become another using Rotations, Reflections, or Translations, then the shapes are Congruent.
Rotation (Turn)
Reflection (Flip)
Translation (Shift)
Even after these transformations, the shape still has the same size, angles, area and line lengths. Hence, they are congruent.
Angles can be congruent as well. Congruent angles have the same angle measurs as each other. They are present in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines.
They are denoted by the symbol “≅”, so if we want to represent ∠A is congruent to ∠B, we will write it as ∠A ≅ ∠B.