Similar and Congruent Figures
Similar and congruent figures are fundamental geometry concepts introduced in Grade 4, Saxon Math Intermediate 4 Chapter 7. Two figures are similar (~) when they share the same shape with equal corresponding angles but proportional side lengths (like a photo zoomed in or out). Two figures are congruent (≅) when they have both the same shape and the same size—every corresponding angle and side length matches exactly. For example, two triangles with sides 5 cm, 12 cm, and 13 cm are congruent, not just similar.
Key Concepts
New Concept Figures that are the same shape are similar . Figures that are the same shape and the same size are congruent .
What’s next Next, you’ll apply these definitions to identify similar and congruent shapes among triangles, rectangles, and real world signs.
Common Questions
What is the difference between similar and congruent figures?
Similar figures have the same shape with proportional sides but can be different sizes. Congruent figures have the same shape AND the same size—all matching angles and side lengths are equal.
How do I remember the difference between similar and congruent?
Remember that Congruent figures are Copies of each other (same shape and size). Similar figures are the Same Shape but can be scaled up or down like a zoom function.
Can congruent figures also be similar?
Yes. All congruent figures are also similar because they have the same shape. But not all similar figures are congruent, since similar figures can differ in size.
What symbols are used for similar and congruent figures?
The tilde symbol (~) means similar. The congruence symbol (≅) means congruent.
If two triangles have angles of 60, 60, and 60 degrees each, are they similar, congruent, or both?
They are always similar because they have the same shape. They are congruent only if their side lengths are also equal.