# Congruent vs. Similarity: What's the Difference?

Edited by Aimie Carlson || By Janet White || Published on December 1, 2023
Congruent shapes are identical in size and shape, while similar shapes have the same shape but different sizes.

## Key Differences

Congruent shapes are exactly the same in both size and shape, meaning all corresponding sides and angles are equal. Similarity in geometry refers to shapes that have the same shape but can be different sizes; they have proportional sides and equal angles.
In congruent figures, every detail of their geometry matches, including the lengths of sides and measures of angles. Similar figures maintain the same shape, but their sizes can scale up or down, like a photograph resized but keeping its proportions.
The concept of congruence is strict, requiring a perfect match, often shown by overlaying one shape onto another. Similarity, however, allows for more flexibility, as long as the basic shape remains consistent and angles are congruent.
Congruent figures can be reflected, rotated, or translated and still remain congruent. Similar figures can undergo the same transformations, plus resizing, while maintaining their similarity.
Congruence is a term often used in math, especially in geometry, to describe perfect correspondence between figures. Similarity also has broad applications in geometry, used to solve problems involving figures that are alike in shape but vary in size.

## Comparison Chart

### Size and Shape

Identical in size and shape.
Same shape, different sizes.

### Side Lengths

All corresponding sides are equal.
Sides are proportional.

### Angle Measures

All corresponding angles are equal.
Angles are congruent.

### Transformations

Includes rotation, reflection, translation.
Includes scaling in addition to rotations, reflections, translations.

### Geometric Strictness

Requires exact match.
Allows scaling while preserving shape.

## Congruent and Similarity Definitions

#### Congruent

Congruent figures match in all geometric properties.
The congruent rectangles on the page have the same length and width.

#### Similarity

Similar shapes have the same form but different sizes.
The two triangles are similar, sharing the same angles but different side lengths.

#### Congruent

Congruence implies perfect overlay of shapes.
These congruent circles can be superimposed exactly.

#### Similarity

Similarity in geometry means proportional dimensions.
The similarity between the two buildings is seen in their proportional designs.

#### Congruent

Congruent angles have the same degree measurement.
The angles of these congruent pentagons measure identically.

#### Similarity

Similarity includes figures that are scaled versions of each other.
These similar rectangles have the same shape but are scaled differently.

#### Congruent

Congruent shapes are identical in size and shape.
The two triangles are congruent, having three equal sides and angles.

#### Similarity

Similar angles in different figures are congruent.
Despite their size difference, the similar triangles have equal angles.

#### Congruent

Congruent objects are mirror images or exact duplicates.
The congruent squares fit perfectly into each other.

#### Similarity

The quality or condition of being similar; resemblance.

#### Congruent

Corresponding; congruous.

#### Similarity

A corresponding aspect or feature; equivalence
A similarity of writing styles.

#### Congruent

Coinciding exactly when superimposed
Congruent triangles.

#### Similarity

Closeness of appearance to something else.

#### Similarity

(philosophy) The relation of sharing properties.

#### Similarity

(maths) A transformation that preserves angles and the ratios of distances

#### Similarity

The property of two matrices being similar.

#### Similarity

The quality or state of being similar; likeness; resemblance; as, a similarity of features.
Hardly is there a similarity detected between two or three facts, than men hasten to extend it to all.

#### Similarity

The quality of being similar

#### Similarity

A Getalt principle of organization holding that (other things being equal) parts of a stimulus field that are similar to each other tend to be perceived as belonging together as a unit

#### Similarity

Similar figures maintain the same shape when scaled.
The model is a smaller, similar replica of the original structure.

## FAQs

#### Is congruence the same as equality?

In geometry, yes, it means exactly equal in size and shape.

#### What are congruent angles?

Angles that have the same measure.

#### Can two shapes be similar and congruent?

No, congruent shapes are identical in size, while similar shapes vary in size.

#### Can circles be congruent?

Yes, if they have the same radius.

#### Are all congruent figures similar?

Yes, but not all similar figures are congruent.

#### What is required for two triangles to be similar?

They must have the same angles and proportional sides.

#### Are all similar figures the same shape?

Yes, but their sizes are different.

#### What does congruent mean in geometry?

Exact match in size and shape.

#### How do you prove congruence?

By showing all corresponding sides and angles are equal.

#### Can congruent figures be mirror images?

Yes, they can be reflections and still be congruent.

#### What is the symbol for congruence?

It's denoted by an equal sign with a tilde above it (≅).

#### What is a real-world example of congruence?

Identical twins are an example of congruence in physical features.

#### Do similar objects have to be geometric?

Typically, but the concept can apply more broadly.

#### Can congruence apply to non-geometric objects?

In a broader sense, it can refer to agreement or harmony in non-geometric contexts.

#### Can a square and rectangle be similar?

No, because their shapes are fundamentally different.

#### Why is understanding similarity important?

It's key in scaling models and understanding proportions.

#### What does similarity mean in geometry?

Shapes having the same form but different sizes.

#### What transformations maintain congruence?

Rotation, reflection, and translation.

#### What is an example of similarity in nature?

Leaves on a tree can be similar but differ in size.

#### How is congruence used in construction?

To ensure parts fit together precisely.