Congruent vs. Equal — What's the Difference?

Shapes that are congruent can be overlaid precisely.

Applies to numbers, algebraic expressions, etc.

Involves physical dimensions like length and angle.

Equal values can be substituted for each other in equations.

Represented by ≅ in geometry.

Values that are equal represent the same quantity.

Specific postulates or theorems apply, such as ASA or SSS for triangles.

Equality is determined through logical deduction or algebraic proof.

Can involve rotations, reflections, or translations without altering congruency.

Represented by = in mathematics.

Corresponding; congruous.

Being the same in quantity, size, degree, or value

Coinciding exactly when superimposed

Having the ability or resources to meet (a challenge)

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 person or thing that is the same as another in status or quality

Corresponding in character; congruous

Be the same as in number or amount

Harmonious.

Having the same quantity, measure, or value as another.

(mathematics) Having a difference divisible by a modulus.

(Mathematics) Being the same or identical to in value.

(mathematics) Coinciding exactly when superimposed.

Having the same privileges, status, or rights

(algebra) Satisfying a congruence relation.

Being the same for all members of a group

Possessing congruity; suitable; agreeing; corresponding.

Having the requisite qualities, such as strength or ability, for a task or situation

Corresponding in character or kind

Similar to or the same as another, as in ability

Coinciding when superimposed

One that is equal to another

To be equal to, especially in value.

To do, make, or produce something equal to

(not comparable) The same in all respects.

Exactly identical, having the same value.

(obsolete) Fair, impartial.

(comparable) Adequate; sufficiently capable or qualified.

(obsolete) Not variable; equable; uniform; even.

(music) Intended for voices of one kind only, either all male or all female; not mixed.

To be equal to, to have the same value as; to correspond to.

(transitive) To make equivalent to; to cause to match.

(informal) To have as its consequence.

A person or thing of equal status to others.

(obsolete) State of being equal; equality.

Agreeing in quantity, size, quality, degree, value, etc.; having the same magnitude, the same value, the same degree, etc.; - applied to number, degree, quantity, and intensity, and to any subject which admits of them; neither inferior nor superior, greater nor less, better nor worse; corresponding; alike; as, equal quantities of land, water, etc. ; houses of equal size; persons of equal stature or talents; commodities of equal value.

Bearing a suitable relation; of just proportion; having competent power, abilities, or means; adequate; as, he is not equal to the task.

Not variable; equable; uniform; even; as, an equal movement.

Evenly balanced; not unduly inclining to either side; characterized by fairness; unbiased; impartial; equitable; just.

Of the same interest or concern; indifferent.

Intended for voices of one kind only, either all male or all female; - opposed to mixed.

Exactly agreeing with respect to quantity.

One not inferior or superior to another; one having the same or a similar age, rank, station, office, talents, strength, or other quality or condition; an equal quantity or number; as, "If equals be taken from equals the remainders are equal."

State of being equal; equality.

To be or become equal to; to have the same quantity, the same value, the same degree or rank, or the like, with; to be commen urate with.

To make equal return to; to recompense fully.

To make equal or equal to; to equalize; hence, to compare or regard as equals; to put on equality.

A person who is of equal standing with another in a group

Be identical or equivalent to;

Be equal to in quality or ability;

Make equal, uniform, corresponding, or matching;

Well matched; having the same quantity, value, or measure as another;

Equal in amount or value;

Congruent figures are "equal" in terms of their geometrical properties like size and shape, but the term "equal" is more commonly used to refer to numerical or quantitative equality.

Two triangles can be proven congruent using criteria like Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Side-Side-Side (SSS), among others.

Congruence is fundamental in geometry for comparing shapes, solving problems, and proving theorems, ensuring that figures maintain their properties under various transformations.

An example in algebra would be showing that two expressions, such as x+5 and 3x−2, are equal for a specific value of x, say when x=7.

Congruence and equality are related concepts used to describe sameness, with congruence referring to geometrical similarity and equality to numerical or quantitative sameness.

Two shapes are congruent if they have the same size and shape, meaning their corresponding angles and sides are equal, and they can be perfectly overlapped.

The term "congruent" is not typically used to describe numbers. Instead, numbers are described as equal if they have the same value.

Equality can refer to specific properties of geometric figures, like the lengths of sides or measures of angles, but it does not describe the overall geometric congruence of figures.

Yes, congruent figures can be rotated, reflected, or translated, changing their orientation but not their congruency.

Congruent figures can differ in color, texture, or pattern, as congruence only concerns their geometric properties, not their appearance.