Congruent vs. Similar — What's the Difference?

Identical in form and dimensions.

Proportionally equivalent in shape but not size.

Having the exact same size and shape.

Having angles that are exactly alike.

Equal in all geometrical aspects.

Figures scaled up or down without altering shape.

Matching completely in terms of geometry.

Corresponding in shape, differing in dimensions.

Exactly superimposable figures.

Maintaining shape but varying in size.

Corresponding; congruous.

Having a resemblance in appearance, character, or quantity, without being identical

Coinciding exactly when superimposed

A person or thing similar to another

Of or relating to two numbers that have the same remainder when divided by a third number. For example, 11 and 26 are congruent when the modulus is 5.

A substance that produces effects resembling the symptoms of particular diseases (the basis of homeopathic treatment)

Corresponding in character; congruous

Having a resemblance in appearance or nature; alike though not identical.

Harmonious.

(Mathematics) Having corresponding angles equal and corresponding line segments proportional. Used of geometric figures

(mathematics) Having a difference divisible by a modulus.

Having traits or characteristics in common; alike, comparable.

(mathematics) Coinciding exactly when superimposed.

(mathematics) Of geometrical figures including triangles, squares, ellipses, arcs and more complex figures, having the same shape but possibly different size, rotational orientation, and position; in particular, having corresponding angles equal and corresponding line segments proportional; such that one can be had from the other using a sequence of rotations, translations and scalings.

(algebra) Satisfying a congruence relation.

Of two square matrices; being such that a conjugation sends one matrix to the other.

Possessing congruity; suitable; agreeing; corresponding.

That which is similar to, or resembles, something else, as in quality, form, etc.

Corresponding in character or kind

(homeopathy) A material that produces an effect that resembles the symptoms of a particular disease.

Coinciding when superimposed

Exactly corresponding; resembling in all respects; precisely like.

Nearly corresponding; resembling in many respects; somewhat like; having a general likeness.

Homogenous; uniform.

That which is similar to, or resembles, something else, as in quality, form, etc.

Marked by correspondence or resemblance;

Having the same or similar characteristics;

Resembling or similar; having the same or some of the same characteristics; often used in combination;

(of words) expressing closely related meanings

Capable of replacing or changing places with something else;

Two shapes are congruent if they are identical in size and shape, allowing them to fit perfectly on each other.

Two triangles are similar if they have the same angles and their sides are in proportion.

Similarity transformations include rotations, translations, and reflections, as well as scaling (enlargement or reduction), which changes the size but not the shape.

Yes, congruent shapes are always similar because they have identical angles and proportional sides (in this case, the proportion is 1:1).

Understanding congruence and similarity helps students develop spatial reasoning, solve real-world problems involving dimensions, and comprehend the properties of different geometrical shapes.

Similar shapes have the same angles and proportional sides but differ in size, whereas congruent shapes are identical in both size and shape.

Congruence is vital in ensuring parts fit perfectly in manufacturing, while similarity helps in understanding scales and proportions in various fields like architecture and design.

Triangles are similar if they have corresponding angles equal and the sides around those angles in proportional lengths, satisfying angle-angle (AA) or side-angle-side (SAS) proportionality.

Congruence is preserved through rotations, translations, and reflections, where the shape and size of figures remain unchanged.

Two polygons are similar if their corresponding angles are equal and their corresponding side lengths are proportional.

Symmetry often involves congruence, where each symmetric part is identical in size and shape to its counterpart. Similarity relates to symmetry when scaling transformations are considered, maintaining shape but altering size.

All circles are similar as they differ only in size, not in shape. Circles are congruent when they have the same radius.

Triangles are congruent if they meet any of the following criteria: side-side-side (SSS), side-angle-side (SAS), or angle-side-angle (ASA).

Professions such as architecture, engineering, graphic design, and any field involving drafting or 3D modeling greatly benefit from an understanding of congruence and similarity.

Tools like geometric software, transparent overlays, geometric solids, and rulers and protractors can be used to visually and practically demonstrate the principles of congruence and similarity to students.