HSG.CO.A.3: Rotations and Reflections That Carry a Polygon onto Itself
In plain English: HSG.CO.A.3 is the Common Core geometry standard that asks students to describe the rotations and reflections that carry a rectangle, parallelogram, trapezoid or regular polygon onto itself. Students name each line of reflection and each center and angle of rotation, and explain why other lines and angles fail. It is usually taught in high school Geometry.
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Common Core State Standards for Mathematics · Domain: Congruence (CO) · Cluster: Experiment with transformations in the plane Also written as HSG-CO.A.3 or G-CO.3 · Official standard
Students find every rotation and reflection that carries a figure onto itself, meaning that after the motion the figure occupies exactly the same set of points it did before. They work through the four families the standard names: rectangles, parallelograms, trapezoids and regular polygons. For each figure they name the lines of reflection and the center and angles of rotation, and they explain why lines and angles that look plausible, such as the diagonal of a rectangle, do not work.
Students test symmetries three ways: by turning and flipping tracing paper, by checking vertex coordinates under rules such as (x, y) → (-x, y), and by using geometry software. The lesson ends with the pattern for regular polygons: a regular polygon with n sides has n lines of reflection and is carried onto itself by rotations of 360°/n and its multiples.
Learning Objectives
By the end of this lesson, students will be able to:
Describe every rotation and reflection that carries a given rectangle, parallelogram, trapezoid or regular polygon onto itself
Locate the center of rotation and each line of reflection precisely, for example as the intersection of the diagonals or the line through the midpoints of opposite sides
Explain with a counterexample why a proposed line or angle does not carry a figure onto itself
Verify a symmetry with coordinates by showing that the set of vertices maps onto itself
State and use the rotation angles 360°/n and the n lines of reflection of a regular n-gon
Prior Knowledge Required
Students should already be comfortable with:
Recognizing and drawing lines of symmetry 4.G.A.3
Properties of rotations and reflections verified with tracing paper 8.G.A.1
Transformations as functions on points and coordinate rules HSG.CO.A.2
Classifying quadrilaterals in a hierarchy, for example every square is a rectangle and a rhombus 5.G.B.4
Give each student a paper rectangle that is not a square (for example 10 cm by 5 cm) with one corner marked with a dot on the front.
Warm-Up Prompt
"Find every way to pick up the rectangle and put it back so that it fits its outline exactly. You may turn it or flip it. For each way, where does the dotted corner end up?"
Students find four positions: the original, a half turn, a flip over the long direction and a flip over the short direction. The dot visits each corner exactly once, which is a useful check that the list is complete. Many students also try folding along a diagonal; let them fold and see that the corners do not match. Introduce the phrase "carries the figure onto itself".
Direct Instruction20 minutes
Define: a rigid motion carries a figure onto itself when the image is exactly the same set of points as the figure. For a polygon, it is enough to check that the vertices land on vertices and that sides go to sides. Every figure is carried onto itself by the 360° rotation (the identity), so the interesting question is what else works. Use Diagram 1 and Diagram 2 with these examples:
Rectangle
Rectangle with vertices (-4, -2), (4, -2), (4, 2), (-4, 2). Test the axes, the 180° rotation about the origin and the diagonal through (-4, -2) and (4, 2).
Equation: Reflections across y = 0 and x = 0 and the 180° rotation work; reflecting (4, -2) across the diagonal gives (0.8, 4.4), not a vertex
Parallelogram
Parallelogram with vertices (0, 0), (6, 0), (8, 3), (2, 3). Its diagonals meet at (4, 1.5).
Equation: 180° rotation about (4, 1.5): (x, y) → (8 - x, 3 - y) sends (0, 0) to (8, 3) and (6, 0) to (2, 3); no reflection works
Isosceles trapezoid
Trapezoid with vertices (-4, 0), (4, 0), (2, 3), (-2, 3), legs of equal length.
Equation: Reflection across x = 0 works; the 180° rotation about (0, 1.5) sends (-4, 0) to (4, 3), not a vertex
Regular hexagon
Rotations about the center and lines of reflection.
Equation: Rotations of 60°, 120°, 180°, 240°, 300° (360°/6 = 60°) and 6 lines of reflection
Regular pentagon
Rotations about the center and lines of reflection.
Equation: Rotations of 72°, 144°, 216°, 288° (360°/5 = 72°) and 5 lines, each through a vertex and the midpoint of the opposite side
Stress three points. First, the center of rotation for a rectangle or parallelogram is the point where the diagonals intersect. Second, a general trapezoid has no symmetry except the identity; only an isosceles trapezoid has a line of reflection. Some textbooks define a trapezoid as having at least one pair of parallel sides, which makes every parallelogram a trapezoid; say which definition your course uses. Third, for a regular polygon with an even number of sides, half the lines pass through opposite vertices and half through midpoints of opposite sides; with an odd number, every line passes through a vertex and the midpoint of the opposite side.
Guided Practice15-20 minutes
Pairs describe all the symmetries of three figures and verify one reflection and one rotation with coordinates:
Square with vertices (0, 0), (4, 0), (4, 4), (0, 4): rotations of 90°, 180° and 270° about (2, 2), and 4 lines of reflection: x = 2, y = 2 and both diagonals. A square is a regular polygon, so it has 4 lines and rotations by multiples of 90°.
Rhombus with vertices (0, 3), (4, 0), (0, -3), (-4, 0): the 180° rotation about the origin and reflections across both diagonals, which here are the axes. A rhombus is a parallelogram, and it is the kind of parallelogram that does have lines of reflection.
Trapezoid with vertices (-3, 0), (5, 0), (3, 2), (0, 2): the legs have lengths √13 and √8, so it is not isosceles and only the 360° rotation carries it onto itself.
Ask each pair to write its evidence as a mapping of vertices, for example "(0, 3) → (0, -3)". Listen for students who check only one vertex; all of them must land on vertices.
Independent Practice15 minutes
Students work alone on two tasks. (1) Rectangle with vertices (0, 0), (10, 0), (10, 4), (0, 4): give the equations of both lines of reflection, the center of the 180° rotation, and the vertex mapping for each. (Answer: x = 5 and y = 2, center (5, 2).) (2) Regular heptagon: list the rotation angles less than 360° to the nearest tenth of a degree, and describe the 7 lines of reflection. (Answer: multiples of 360°/7 ≈ 51.4°: 51.4°, 102.9°, 154.3°, 205.7°, 257.1°, 308.6°; each line passes through a vertex and the midpoint of the opposite side.)
Closure5 minutes
Exit ticket: (1) Name a quadrilateral that is carried onto itself by a 180° rotation but by no reflection. (A parallelogram that is not a rectangle or a rhombus.) (2) Name a quadrilateral with a line of reflection but no rotation other than 360°. (An isosceles trapezoid.) (3) What is the smallest positive rotation that carries a regular polygon with 20 sides onto itself, and how many lines of reflection does it have? (18°, and 20 lines.)
Differentiation Strategies
For Struggling Students
Have students number the vertices of a cut-out figure on both sides so they can see where each vertex goes after a turn or flip
Provide a recording table with columns for the motion, its center or line, and the vertex mapping
Start with the rectangle and the square before the parallelogram and the trapezoid
For Advanced Students
Ask students to prove that if a quadrilateral is carried onto itself by a 180° rotation about a point, then it is a parallelogram
Ask students to count all the symmetries of a regular n-gon (rotations including 360° plus reflections) and explain why the total is 2n
Ask whether a figure can have exactly two lines of reflection that are not perpendicular, and to justify the answer
Assessment Guidance
What to Look For
Complete descriptions name the center and angle of every rotation and give each line of reflection precisely (an equation, or "the line through the midpoints of AB and CD"), not just "it has symmetry". Check that students reject the diagonals of a non-square rectangle and do not claim reflections for a general parallelogram. For regular polygons, look for the angle 360°/n and all its multiples below 360°, and for the correct description of where the lines pass for odd and even n.
02
Classroom Activities
3 Activities
1
Trace, Turn and Flip
20 minPairs
Pairs use tracing paper and a pushpin to find every rotation and reflection that carries four quadrilaterals onto themselves, then compare the results.
Materials per Pair
4 cut-out quadrilaterals: a rectangle that is not a square, a parallelogram with no right angles and unequal adjacent sides, an isosceles trapezoid, and a trapezoid that is not isosceles
Tracing paper, a pushpin and a ruler
Procedure
Trace a figure, then look for a point where you can pin the tracing and turn it so it fits the figure again; record the center and the angle
Look for lines where you can flip the tracing over so it fits again; draw each line on the figure
Mark one vertex with a dot and record where it goes under every motion you find
Complete a class chart with the number of rotations (including 360°) and the number of reflections for each figure
Discussion Questions
Which figures have a line of reflection but no half-turn? Which have a half-turn but no line of reflection?
Why can a pin placed anywhere other than the intersection of the diagonals never work for the rectangle?
2
Regular Polygon Pattern Hunt
20 minGroups of 3-4
Groups use pattern blocks or printed regular polygons with 3, 4, 5 and 6 sides to find the rotations and lines of reflection of each, then look for a rule that predicts them for any number of sides.
Procedure
Trace each polygon, mark its center, and turn the tracing until the polygon fits again; record the smallest angle that works
Fold paper copies to find every line of reflection and sketch where each line crosses the polygon: through a vertex, through the midpoint of a side, or both
Fill in a table with the number of sides n, the smallest rotation angle and the number of lines
Use the pattern to predict the smallest rotation and the number of lines for a regular polygon with 24 sides (15° and 24 lines), and justify the prediction
Challenge Variation
Groups explain why the lines of reflection look different for odd and even n, using the idea that a line through the center must reach either a vertex or the midpoint of a side on the far side.
3
Symmetry Check with Coordinates and Software
20 minPairs
Pairs place three quadrilaterals on a coordinate grid in geometry software, apply the reflect and rotate tools, and confirm each symmetry by checking that every vertex lands on a vertex.
The 3 Figures
Rectangle (1, 1), (7, 1), (7, 4), (1, 4): lines x = 4 and y = 2.5, and 180° about (4, 2.5)
Parallelogram (0, 0), (5, 0), (7, 3), (2, 3): 180° about (3.5, 1.5) only
Isosceles trapezoid (1, 0), (7, 0), (6, 3), (2, 3): the line x = 4 only
Procedure
Construct each figure and apply the motion listed; check that the image covers the figure exactly
Try one motion that fails for each figure and record the vertex that lands off the figure
Write each successful symmetry as a coordinate rule, for example (x, y) → (8 - x, y) for the reflection across x = 4
Modification for Distance Learning
Share one geometry software file with the three figures already built; pairs record their vertex mappings in a shared table.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Symmetries of a Rectangle, a Parallelogram and an Isosceles Trapezoid
Drawn to scale from the coordinates in the worked examples. Dashed blue lines are lines of reflection and the blue dot is a center of rotation. The dotted red diagonal of the rectangle is not a line of reflection, and the parallelogram has only its 180° rotation about the intersection of its diagonals.
Diagram 2: Rotations and Lines of Reflection of Regular Polygons
A regular hexagon has 6 lines of reflection and is carried onto itself by rotations of 60° and its multiples about the center. A regular pentagon has 5 lines, each through a vertex and the midpoint of the opposite side, and rotations of 72° and its multiples.
04
Homework Assignment
~30 min
HSG.CO.A.3 Homework: Rotations and Reflections That Carry a Figure onto Itself
Directions: For every figure, describe each rotation (center and angle) and each reflection (the line) that carries it onto itself, not counting the 360° rotation unless asked. Support each answer with a vertex mapping, and use a specific vertex to show why a proposed motion fails.
Part 1: Rectangles, Parallelograms and Trapezoids (Problems 1-3)
A rectangle has vertices (-6, -3), (6, -3), (6, 3) and (-6, 3). (a) Describe every rotation and reflection that carries it onto itself, with a coordinate rule for each. (b) Show that reflecting (6, -3) across the diagonal through (-6, -3) and (6, 3) does not give a vertex.
A parallelogram has vertices (-1, -2), (5, -2), (7, 2) and (1, 2). (a) Find the center of the 180° rotation that carries it onto itself and show where each vertex goes. (b) Show that the reflection across the vertical line x = 3 does not carry it onto itself.
Compare two trapezoids: the isosceles trapezoid (-6, 0), (6, 0), (3, 5), (-3, 5) and the right trapezoid (0, 0), (8, 0), (5, 4), (0, 4). Describe the rotations and reflections that carry each onto itself and explain the difference.
Part 2: Regular Polygons (Problems 4-6)
A regular octagon is centered at point O. (a) List every rotation about O less than 360° that carries it onto itself. (b) How many lines of reflection does it have, and where do they pass? (c) If vertex 1 is rotated 135° counterclockwise, which vertex does it land on (vertices numbered counterclockwise)?
(a) Describe all the rotations and reflections that carry an equilateral triangle onto itself. (b) A regular polygon has 36 sides. What is the smallest positive rotation that carries it onto itself, and how many lines of reflection does it have?
Make a table for a square, a rhombus that is not a square, a rectangle that is not a square, a parallelogram with no right angles and unequal adjacent sides, an isosceles trapezoid, and a regular polygon with n sides. For each, give the rotation angles less than 360° and the number of lines of reflection.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Complete List
Every rotation and reflection found, none extra
One motion missing or one extra
Several missing or wrong
Precise Description
Centers, angles and lines stated exactly
Described loosely ("the middle line")
Not described
Coordinate Evidence
Correct vertex mappings and counterexamples
Mappings with an error
No evidence
Regular Polygon Pattern
Uses 360°/n and n lines correctly
Pattern partly correct
Pattern missing or wrong
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Pick an option on each multiple-choice question to see the explanation; tracing paper helps. Work the short answers on paper, then compare with the answer. Reset quiz clears your choices.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which rotation carries a rectangle that is not a square onto itself?
Answer: B
A half-turn about the point where the diagonals meet swaps opposite vertices, so the rectangle lands on itself. Choice A would turn the long sides into short sides, which only works for a square. Choice C moves the rectangle off its original position.
Question 2 of 20 · Multiple Choice
How many lines of reflection does a rectangle that is not a square have?
Answer: C
The two lines through the midpoints of opposite sides are lines of reflection. Choice D counts the diagonals too, a common error: folding along a diagonal of a non-square rectangle does not match the corners.
Question 3 of 20 · Multiple Choice
A parallelogram has no right angles and its adjacent sides have different lengths. Which motions, other than the 360° rotation, carry it onto itself?
Answer: C
The half-turn about the intersection of the diagonals sends each vertex to the opposite vertex. Such a parallelogram has no line of reflection: choice A describes a rhombus, and choice B describes a rectangle or a rhombus. Choice D forgets the half-turn.
Question 4 of 20 · Multiple Choice
A parallelogram has vertices (1, 1), (7, 1), (9, 5) and (3, 5). What is the center of the 180° rotation that carries it onto itself?
Answer: A
The center is the intersection of the diagonals, which is the midpoint of the diagonal from (1, 1) to (9, 5): (5, 3). It is also the midpoint of (7, 1) and (3, 5). Choice B uses the midpoint of the bottom side's x-values, 1 and 7.
Question 5 of 20 · Multiple Choice
Which line carries an isosceles trapezoid onto itself?
Answer: C
Reflecting across the line through the midpoints of the bases swaps the two legs, which have equal length. Choice B would swap the two bases, which have different lengths. A diagonal (choice A) does not carry the trapezoid onto itself.
Question 6 of 20 · Multiple Choice
A trapezoid has vertices (0, 0), (6, 0), (4, 3) and (1, 3). Which motions carry it onto itself?
Answer: A
Its legs have lengths √10 and √13, so it is not isosceles and has no line of reflection. Choice B fails because it sends (1, 3) to (5, 3), which is not a vertex. Choice C sends (0, 0) to (6, 3), not a vertex, and choice D would swap the bases, which have different lengths.
Question 7 of 20 · Multiple Choice
What is the smallest positive rotation that carries a regular decagon (10 sides) onto itself?
Answer: D
A regular polygon with n sides is carried onto itself by a rotation of 360°/n about its center, and 360°/10 = 36°. Choice B is half of that, and choice A confuses the number of sides with the angle.
Question 8 of 20 · Multiple Choice
How many lines of reflection does a regular polygon with 16 sides have?
Answer: B
A regular n-gon has n lines of reflection. For n = 16, 8 lines pass through opposite vertices and 8 through midpoints of opposite sides, 16 in all. Choice A counts only one of the two kinds of lines.
Question 9 of 20 · Multiple Choice
Which rotation about its center carries a regular nonagon (9 sides) onto itself?
Answer: B
The rotations are the multiples of 360°/9 = 40°: 40°, 80°, 120° and so on. 80° = 2 × 40°. None of 60°, 100° or 45° is a multiple of 40°.
Question 10 of 20 · Multiple Choice
In a regular polygon with an odd number of sides, where does each line of reflection pass?
Answer: C
With an odd number of sides, a vertex always faces a side, never another vertex, so every line runs from a vertex through the center to the midpoint of the opposite side. Choices A and B describe the lines of polygons with an even number of sides.
Question 11 of 20 · Multiple Choice
A square has vertices (3, 3), (-3, 3), (-3, -3) and (3, -3). Which motion does NOT carry it onto itself?
Answer: D
A 45° rotation sends (3, 3) to (0, 3√2), which is not a vertex. The square is a regular polygon with 4 sides, so its rotations are multiples of 90°, and y = x (a diagonal) and the x-axis are two of its 4 lines of reflection.
Question 12 of 20 · Multiple Choice
A rectangle has vertices (-5, -1), (5, -1), (5, 3) and (-5, 3). Which line carries it onto itself?
Answer: A
The center of the rectangle is (0, 1), and the horizontal line of reflection passes through it: y = 1 sends (5, -1) to (5, 3). Choice B, the x-axis, sends (5, 3) to (5, -3), not a vertex; the rectangle is not centered at the origin. Choice C is a diagonal.
Question 13 of 20 · Multiple Choice
A parallelogram has vertices (0, 0), (5, 0), (8, 4) and (3, 4), and all four sides have length 5. Which line carries it onto itself?
Answer: B
Because all sides are equal, this parallelogram is a rhombus, and its diagonals are lines of reflection. Reflecting across the diagonal through (0, 0) and (8, 4) swaps (5, 0) and (3, 4). Choice A sends (0, 0) to (8, 0), not a vertex. Choice D would be right for a parallelogram with unequal adjacent sides.
Question 14 of 20 · Multiple Choice
The smallest positive rotation that carries a regular polygon onto itself is 20°. How many sides does it have?
Answer: C
The smallest rotation is 360°/n, so 360°/n = 20° gives n = 18. Choice A confuses the angle with the number of sides, and choice B uses 180° instead of 360°.
Question 15 of 20 · Short Answer
A rectangle measures 10 cm by 6 cm. Describe every rotation and reflection that carries it onto itself, and explain why a diagonal is not a line of reflection.
Rotations: 180° (and 360°) about the intersection of the diagonals. Reflections: across the line through the midpoints of the 10 cm sides and across the line through the midpoints of the 6 cm sides. A diagonal does not cut the 90° corner angles in half (it makes angles of about 31° and 59° with the sides), so reflecting across diagonal AC does not send side AB onto side AD. With A(0, 0), B(10, 0), C(10, 6) and D(0, 6), the reflection sends B to about (4.7, 8.8), outside the rectangle, so the corners do not match.
Question 16 of 20 · Short Answer
A parallelogram has vertices A(-2, 0), B(4, 0), C(6, 4) and D(0, 4). Find the center of the rotation that carries it onto itself and show where each vertex goes.
The diagonals AC and BD both have midpoint (2, 2). The 180° rotation about (2, 2) is (x, y) → (4 - x, 4 - y). It sends A → C, B → D, C → A and D → B: for example, A(-2, 0) goes to (6, 4) = C.
Question 17 of 20 · Short Answer
An isosceles trapezoid has vertices (-5, 0), (5, 0), (3, 4) and (-3, 4). Describe the reflection that carries it onto itself and show it with coordinates. Why does a 180° rotation not work?
The reflection across the y-axis, (x, y) → (-x, y), swaps (-5, 0) with (5, 0) and (3, 4) with (-3, 4). The 180° rotation about (0, 2), the center of the figure, sends (-5, 0) to (5, 4), which is not a vertex: a half-turn would swap the bases, and they have different lengths (10 and 6).
Question 18 of 20 · Short Answer
Describe every rotation less than 360° and every reflection that carries a regular dodecagon (12 sides) onto itself.
Rotations about the center by multiples of 360°/12 = 30°: 30°, 60°, 90°, ..., 330° (11 rotations).12 lines of reflection: 6 through pairs of opposite vertices and 6 through the midpoints of pairs of opposite sides.
Question 19 of 20 · Short Answer
The smallest positive rotation that carries a regular polygon onto itself is 24°. How many sides does it have, how many lines of reflection, and where do the lines pass?
360°/n = 24° gives n = 15 sides, so it has 15 lines of reflection. Because 15 is odd, each line passes through a vertex, the center and the midpoint of the opposite side.
Question 20 of 20 · Short Answer
Counting the 360° rotation, how many rotations and reflections carry each figure onto itself: a parallelogram with no right angles and unequal adjacent sides, an isosceles trapezoid, a rectangle that is not a square, and a regular hexagon? Order them from fewest to most.
Parallelogram: 2 (360° and 180°). Isosceles trapezoid: 2 (360° and one reflection). Rectangle: 4 (360°, 180° and two reflections). Regular hexagon: 12 (six rotations including 360°, and six reflections). Order: parallelogram and isosceles trapezoid (tie, 2 each), rectangle (4), regular hexagon (12).
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSG.CO.A.3 mean?
HSG.CO.A.3 means students can list and describe every rotation and reflection that maps a rectangle, parallelogram, trapezoid or regular polygon exactly onto itself. A complete answer names the center and angle of each rotation and the exact position of each line of reflection.
What does "carry a figure onto itself" mean?
It means that after the motion, the figure covers exactly the same points it covered before. The vertices may trade places, but the outline is unchanged. The 360° rotation always does this, so it is usually mentioned but not counted as an interesting symmetry.
Why is the diagonal of a rectangle not a line of symmetry?
Because a diagonal of a rectangle that is not a square does not cut the corner angles in half. Reflecting across it therefore sends the other two corners to points outside the rectangle, and the image does not fit the original. Folding a paper rectangle along its diagonal shows this quickly: the flaps do not line up. Among rectangles, only a square, whose sides are all equal, has its diagonals as lines of reflection.
Does a parallelogram have line symmetry?
Not in general: a parallelogram with no right angles and unequal adjacent sides has only a 180° rotation about the intersection of its diagonals. Special parallelograms do have lines of reflection: a rectangle has two, a rhombus has two (its diagonals), and a square has four.
What symmetries does a trapezoid have?
A trapezoid that is not isosceles has none except the 360° rotation. An isosceles trapezoid has exactly one line of reflection, through the midpoints of the two bases. Under the inclusive definition (at least one pair of parallel sides), parallelograms also count as trapezoids and have their own symmetries, so it helps to say which definition a problem uses.
How many lines of symmetry does a regular polygon have?
A regular polygon with n sides has n lines of reflection and is carried onto itself by rotations of 360°/n and its multiples. For even n, half the lines pass through opposite vertices and half through midpoints of opposite sides. For odd n, each line passes through a vertex and the midpoint of the opposite side.
Is HSG.CO.A.3 the same as the grade 4 symmetry standard?
No, it goes further. In grade 4 (4.G.A.3) students recognize and draw lines of symmetry by folding. HSG.CO.A.3 adds rotations, asks for a complete and precise list of motions for specific families of polygons, and treats those motions as transformations of the plane.
What is a common mistake on symmetry questions?
Giving an incomplete list. Students often find the lines of reflection but forget rotations, or list only the smallest rotation of a regular polygon instead of all its multiples below 360°. Another frequent error is using the wrong center, such as a vertex instead of the intersection of the diagonals.
How can students check their answers?
Use tracing paper or coordinates. Trace the figure, apply the motion to the tracing, and check that it fits exactly. With coordinates, apply the rule to every vertex and check that the set of image vertices is the same as the original set.
Where do these symmetries show up later?
They support proofs about parallelograms in HSG.CO.C.11, where a 180° rotation explains why opposite sides and angles are congruent, and constructions of regular polygons inscribed in circles in HSG.CO.D.13. They also appear in design, from floor tiles to logos.
07
Related Standards
6 standards
These standards connect to HSG.CO.A.3: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
4.G.A.3Prerequisite
Recognize and draw lines of symmetry of two-dimensional figures
Lesson coming soon
8.G.A.1Prerequisite
Verify experimentally the properties of rotations, reflections and translations
