8.G.2: Congruence by Rigid Motions
Also written as 8.G.A.2 and CCSS.MATH.CONTENT.8.G.A.2 · Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software.
The Official Wording
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Common Core State Standards, Grade 8, Geometry · Read it at the source · Checked October 14, 2026
What 8.G.2 Means in Plain English
Eighth graders call two figures congruent when tracing paper can slide, turn or flip one exactly onto the other. They name the moves in order, like “reflect across the x-axis, then translate 3 units left,” and check that each vertex lands on its partner.
A figure that needs stretching is not congruent, however close it looks. Congruence as rigid motion becomes the foundation of high school geometry, where the triangle tests SSS, SAS and ASA are proved from it (HSG-CO.8).
8.G.2 I Can Statements
- I can tell whether two figures are congruent using rigid motions.
- I can describe a sequence of moves that maps one figure onto another.
- I can name each move fully: its line, distance or angle.
8.G.2 Worked Example
Two right triangles in different quadrants, facing opposite ways, and the two moves that bring one onto the other.
Triangle ABC has A(1, 2), B(4, 2), C(1, 4). Triangle DEF has D(−1, −1), E(−4, −1), F(−1, 1). Describe a sequence of rigid motions that maps ABC onto DEF.
- First check that it is worth looking: matching sides must be equal. Both triangles have a horizontal leg of 3 and a vertical leg of 2.AB = DE = 3, AC = DF = 2
- ABC points right from A, but DEF points left from D, so the triangle has been flipped. Reflect it across the y-axis.(x, y) → (−x, y): (−1, 2), (−4, 2), (−1, 4)
- Each image point now sits exactly 3 units above its partner in DEF, so slide everything down 3.(x, y) → (x, y − 3): (−1, −1), (−4, −1), (−1, 1)
- Those are D, E and F, in order, so the sequence works.A → D, B → E, C → F
Check it: Try the other order: translating down 3 first gives (1, −1), (4, −1), (1, 1), and reflecting those across the y-axis lands on D, E and F too. More than one sequence can work.
Common Mistakes with 8.G.2
Matching the wrong vertices
A sent to E and B sent to D, and then no sequence seems to work
Try this: Pair the vertices first: the side of length 3 goes to the side of length 3, the right angle to the right angle.
Describing the moves too loosely
“Flip it and move it down.”
Try this: Name every move completely: a reflection needs its line, a translation its distance and direction, a rotation its center, angle and direction.
Calling a resized copy congruent
A triangle with legs 3 and 2 called congruent to one with legs 6 and 4, because the shapes match
Try this: Compare one pair of matching sides first. If any length changed, no slide, turn or flip can fit them, so they are not congruent.
Where 8.G.2 Fits
Practice 8.G.2
Quick Check
- Square PQRS is translated 5 units left. Is the image congruent to PQRS?
- Triangle A has vertices (0, 0), (2, 0), (0, 3). Triangle B has (0, 0), (0, 2), (−3, 0). What single move maps A onto B?
- Two rectangles measure 4 by 6 and 6 by 4. Are they congruent?