Meaning & use
congruent circles
Last updated
Meanings
nounpluraltechnicalmathematics
Two or more circles that have exactly the same radius, so one can be moved to fit exactly on the other.
Grammar: Used as a plural noun phrase; a single one is 'a congruent circle' only in contrast to another.
Patterns
- congruent circles with radius r
- two congruent circles
The diagram shows two congruent circles of radius 5 cm whose centers are 8 cm apart.
Because the circles are congruent, each has the same area and circumference.
She proved that the three congruent circles all pass through the same point.
adjectivebefore a nountechnicalmathematics
(Of circles) having equal radii, so that the figures are identical in size and shape.
Grammar: Used before a plural noun: congruent circles, but you would not say 'a circle is congruent' without saying what it matches.
Patterns
- congruent circles
- congruent to something
In this construction we need two congruent circles, not just similar ones.
The teacher asked which pairs of drawn circles were congruent.
Common combinations
- two congruent circles
- Draw two congruent circles that overlap slightly.
- a pair of congruent circles
- A pair of congruent circles can be reflected onto each other.
- congruent circles with the same radius
- Congruent circles with the same radius have equal areas.
- prove that the circles are congruent
- You can prove that the circles are congruent by comparing their radii.
Synonyms and how they differ
- equal circles
- Common in older geometry texts for circles of the same radius; 'congruent' stresses that the whole figures match, not only the measurement.
- identical circles
- Everyday wording meaning they look exactly alike; less precise than 'congruent', which is the standard mathematical term.
Opposites
Word family
- congruence noun
- The state of being congruent, especially of geometric figures.
- congruent adjective
- Describing figures that are identical in shape and size.
- congruently adverb
- In a congruent manner; rarely used outside technical writing.
Commonly confused: congruent circles or similar circles?
congruent circles vs similar circles
All circles are similar in the mathematical sense, but only circles with the same radius are congruent; 'similar' allows a change of size, 'congruent' does not.
Practice
Which statement about two congruent circles is always true?
Choose one answer.
Congruent figures are identical in size and shape, so congruent circles must share the same radius. Having the same center is not required (that would make them concentric), intersecting is not guaranteed, and different circumferences would mean different radii, so those circles could not be congruent.
Make it your own
Write a sentence using “congruent circles”, then check it and compare it with the examples above.