Congruent figures have exactly the same size and shape. One can be moved onto the other by sliding, flipping or turning, so every pair of matching sides and angles is equal. Two squares with side 5 are congruent; a 3-4-5 triangle and a 6-8-10 triangle are not, because their sizes differ. The symbol is ≅.
In Spanish
figuras congruentes
Also called
same shape and size, congruent shapes, congruence
How to say it
kon-GROO-ent
Grade level
6-8
Grade 7Grade 8CCSS 8.G.A.2SATACT
Congruent Figures in a picture
The image is turned, but every side and angle matches the original, so the triangles are congruent. Write the letters in matching order: A goes with D, B with E, C with F.
Formal definition and notation
Two plane figures are congruent if one can be obtained from the other by a sequence of rotations, reflections and translations (rigid motions). Rigid motions keep every length and angle measure, so congruent figures have equal corresponding sides and equal corresponding angles. Congruence is written with ≅, and the vertices are listed in matching order: △ ABC ≅ △ DEF means A matches D, B matches E and C matches F.
Symbol
Read it as
Meaning
≅
is congruent to
same size and same shape
△ ABC ≅ △ DEF
triangle A B C is congruent to triangle D E F
the order of the letters shows which vertices match
AB ≅ DE
segment A B is congruent to segment D E
the two segments have the same length
Key facts
Congruence is about measurements, not position: congruent figures can be rotated, reflected, or slid into position and still match perfectly.
Congruent figures have equal perimeters and equal areas. The reverse is false: a 4 by 6 and a 3 by 8 rectangle both have area 24 but are not congruent.
Tick marks show equal sides and arcs show equal angles in a diagram.
For triangles, three shortcuts prove congruence: SSS (three sides), SAS (two sides and the angle between them) and ASA (two angles and the side between them).
Similar figures have the same shape but can differ in size; their sides are proportional. Congruent figures are similar figures with scale factor 1.
Congruent Figuresvs.Equal
Numbers and measures are equal (AB = DE); figures and segments are congruent (AB ≅ DE). Same idea, different objects.
Quick check: 3 questions
Question 1 of 3
Which pair of figures must be congruent?
Show answer and explanation
Answer: B. Circles with the same radius are the same size and shape. Rectangles with the same area can have different sides, equilateral triangles can be any size, and right triangles can have any leg lengths.
Question 2 of 3
△ JKL ≅ △ PQR. Which side has the same length as KL?
Show answer and explanation
Answer: D.K matches Q and L matches R, so KL matches QR. PQ matches JK, PR matches JL, and JL is in the same triangle.
Question 3 of 3
Which transformation does NOT always produce a congruent figure?
Show answer and explanation
Answer: A. A dilation stretches or shrinks a figure, so it changes side lengths (unless the scale factor is 1). Rotations, reflections and translations are rigid motions and keep size and shape.
Congruent Figures: frequently asked questions
How can you tell if two figures are congruent?
Check whether one can be moved exactly onto the other with slides, flips and turns. In practice, compare measurements: if every pair of matching sides and every pair of matching angles is equal, the figures are congruent. For triangles you can use a shortcut such as SSS, SAS or ASA instead of checking all six parts.
What is the difference between congruent and similar?
Congruent figures have the same shape and the same size. Similar figures have the same shape, with equal angles, but their sides may be scaled up or down by the same factor. A 2 by 3 rectangle and a 4 by 6 rectangle are similar but not congruent. Every pair of congruent figures is also similar, with scale factor 1.
Are mirror images congruent?
Yes. A reflection flips a figure but keeps every length and angle, so a figure and its mirror image are congruent. Your left and right hand outlines are a familiar example: they match exactly after a flip, even though you cannot slide one onto the other without flipping it.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 8.G.A.2
Cite this entry
Effortless Math Team. “Congruent Figures.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/congruent-figures/
Flashcard
TermCongruent Figuressame size, same shape
DefinitionFigures that match exactly after sliding, flipping or turning; all matching sides and angles are equal. △ ABC ≅ △ DEF.
CongruentCongruent means exactly the same size and shape. Two segments are congruent when they have the same length, two angles when they have the same measure, and two figures when one can be turned, flipped or slid onto the other. The symbol is ≅: AB ≅ CD reads “segment AB is congruent to segment CD.”Geometry · Grade 8, GeometryRotationA rotation is a transformation that turns a figure around a fixed point, called the center, by a given angle and direction. Every point stays the same distance from the center, so size and shape do not change. About the origin, a 90° counterclockwise turn sends (x, y) to (−y, x).Geometry · Grade 8, GeometryReflectionA reflection is a transformation that flips a figure over a line to make a mirror image. That line is the line of reflection: each point and its image are the same distance from the line, on opposite sides. The image is congruent but faces the other way. Across the y-axis, (x, y) goes to (−x, y).Geometry · Grade 8, GeometryTranslationA translation is a slide: a transformation that moves every point of a figure the same distance in the same direction, without turning or flipping it. The image is congruent to the original. On the coordinate plane, a translation adds the same amounts to every point: (x, y) → (x + a, y + b).Geometry · Grade 8, GeometryLengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2Corresponding AnglesCorresponding angles are two angles in the same relative position at each place where a transversal crosses two lines, such as the top-left corner at both crossings. When the two lines are parallel, corresponding angles are equal. A transversal across two lines makes four pairs of corresponding angles.Geometry · Grade 8, GeometryPerimeterPerimeter is the total distance around a two-dimensional shape. To find it, add the lengths of all the sides. A rectangle with sides 5 and 3 has perimeter 5 + 3 + 5 + 3 = 16. Perimeter is a length, so it uses length units such as inches or meters, never square units.Geometry · Grade 3, Grade 4, Grade 5TriangleA triangle is a polygon with three sides and three angles. Its three corners are called vertices, and the angle measures in any triangle add to 180 degrees. Triangles are classified by their sides (equilateral, isosceles, scalene) and by their angles (acute, right, obtuse).Geometry · Grade 3, Grade 4, Grade 5DilationA dilation is a transformation that enlarges or shrinks a figure by a scale factor k from a fixed center point. Each point moves along the ray from the center to k times its distance. With center at the origin, (x, y) → (kx, ky). The image keeps its shape, so it is similar, not congruent.Geometry · Grade 8, GeometrySimilar FiguresSimilar figures have the same shape but not necessarily the same size. Corresponding angles match, and corresponding side lengths are proportional: each side of one figure is the same multiple, the scale factor, of the matching side of the other. A scale drawing is similar to the real object.Geometry · Grade 7, Grade 8, Algebra 1Scale FactorA scale factor is the number used to multiply side lengths when making a similar figure larger or smaller. A scale factor of 2 doubles every length, and a scale factor of 12 makes lengths half as large. Find it by dividing a new length by the matching original length. Areas change by the square of the scale factor.Ratios and Proportions · Grade 7, Grade 8, Algebra 1QuadrilateralA quadrilateral is a polygon with four straight sides, four vertices and four angles. Its four interior angles always add to 360 degrees. Squares, rectangles, rhombuses, parallelograms, trapezoids and kites are special quadrilaterals, each named for extra properties of its sides or angles.Geometry · Grade 2, Grade 3, Grade 5TransformationA transformation moves or changes a figure on the coordinate plane. The four common transformations are translations (slides), reflections (flips), rotations (turns) and dilations (resizing). The original figure is the preimage and the result is the image, labeled with primes such as A′. Only a dilation changes the size.Geometry · Grade 7, Grade 8, Algebra 1AngleAn angle is formed by two rays that share the same endpoint, called the vertex. It is measured in degrees by how far one ray is turned from the other. A right angle measures 90 degrees, a straight angle measures 180 degrees, and one full turn is 360 degrees.Geometry · Grade 4, Grade 5, Grade 6Coordinate PlaneThe coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin, (0, 0). Every point is located by an ordered pair, x first then y, such as (3, −2). The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.Geometry · Grade 5, Grade 6, Grade 7