HSG.CO.B.6: Rigid Motions and the Definition of Congruence
In plain English: HSG.CO.B.6 is the Common Core geometry standard that asks students to use geometric descriptions of rigid motions to transform figures and to predict what a given rigid motion does to a figure. Students then decide whether two figures are congruent, using the definition that congruent figures are ones that a sequence of rigid motions carries onto each other. It is taught in high school Geometry.
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Common Core State Standards for Mathematics · Domain: Congruence (CO) · Cluster: Understand congruence in terms of rigid motions Also written as HSG-CO.B.6 or G-CO.6 · Official standard
Students use rigid motions described in geometric terms, such as "rotate 90° counterclockwise about vertex A" or "reflect across the line containing side PQ", to transform figures, and they learn to predict the result before drawing it. Because rigid motions keep lengths and angle measures, take lines to lines and keep parallel lines parallel, students can predict image lengths, angles, fixed points and orientation from the description alone.
The lesson then uses the definition of congruence in terms of rigid motions: two figures are congruent when some sequence of rigid motions carries one onto the other. Students decide congruence in both directions. To show two figures are congruent, they give a sequence and test it on every vertex. To show they are not, they find a length or angle that no rigid motion could change.
Learning Objectives
By the end of this lesson, students will be able to:
Transform a figure using a geometric description of a rigid motion, such as a rotation about a vertex or a reflection across the line containing a side
Predict the lengths, angle measures, fixed points and orientation of an image before drawing it
State the definition of congruence in terms of rigid motions
Show that two figures are congruent by giving a sequence of rigid motions that carries one onto the other
Show that two figures are not congruent by finding a measurement that rigid motions preserve but that differs between the figures
Prior Knowledge Required
Students should already be comfortable with:
Definitions of rotations, reflections and translations HSG.CO.A.4
Drawing images and specifying sequences of transformations HSG.CO.A.5
Congruence as a sequence of rotations, reflections and translations in grade 8 8.G.A.2
Post two triangles on a grid: one with vertices (0, 0), (4, 0), (0, 3) and one with vertices (6, 0), (10, 0), (8, 3) (Diagram 2). Do not show the side lengths yet.
Warm-Up Prompt
"Both triangles have a base of 4 units and a height of 3 units. Are they congruent? Decide, then write what evidence would convince a classmate who disagrees."
Many students say yes because the areas match (6 square units each). Let a few students try to cover one triangle with a tracing of the other. Collect the evidence students propose: "same area", "same base", "I could not make them match". Keep the question open. The lesson gives a precise test: congruent means a sequence of rigid motions carries one figure exactly onto the other, and any length that differs rules that out.
Direct Instruction20 minutes
Part 1: What a rigid motion does. Remind students that rotations, reflections and translations are rigid motions. List what every rigid motion does to a figure, so students can predict an image without drawing it:
Lengths and angles are kept: every segment goes to a segment of the same length, and every angle to an angle of the same measure.
Lines stay lines, parallels stay parallel: a line goes to a line, and parallel lines go to parallel lines.
Fixed points follow the description: a rotation fixes its center, a reflection fixes every point of its line, and a translation along a nonzero segment fixes nothing.
Orientation: rotations and translations keep the order of labeled vertices (clockwise stays clockwise); a reflection reverses it.
Part 2: Congruence. State the definition: two figures are congruent if there is a sequence of rigid motions that carries one figure onto the other. To decide, first compare the lengths and angles that must match. If any of them differ, the figures are not congruent, because no rigid motion changes a length or an angle. If they all match, build a sequence and test it on every vertex.
Transform: rotation about a vertex
Rotate △ABC with A(2, 1), B(5, 1), C(2, 3) 90° counterclockwise about vertex A.
Equation: A′ = A(2, 1), B′(2, 4), C′(0, 1). A is the center, so it does not move; side AB, which pointed right, now points up
Transform: reflection across the line of a side
Reflect △PQR with P(2, 0), Q(0, 2), R(4, 4) across the line containing side PQ (Diagram 1).
Equation: P′ = P, Q′ = Q, R′(-2, -2). The line PQ is x + y = 2, and it is the perpendicular bisector of RR′
Predict without drawing
△KLM has KL = 7 cm and m∠L = 48°, with vertices labeled counterclockwise. It is rotated 110° clockwise about a point outside the triangle. Predict K′L′, m∠L′, the orientation and whether K′L′ is parallel to KL.
Equation: K′L′ = 7 cm, m∠L′ = 48°, vertices still counterclockwise; line K′L′ meets line KL at a 70° angle (the supplement of 110°), so they are not parallel
Decide: congruent
Is △ABC with A(1, 1), B(5, 1), C(1, 4) congruent to △DEF with D(-1, 2), E(-1, 6), F(-4, 2)?
Equation: Yes: rotate 90° counterclockwise about the origin, then translate 1 unit up. A → D, B → E, C → F
Decide: not congruent
Is △GHI with G(0, 0), H(4, 0), I(0, 3) congruent to △JKL with J(6, 0), K(10, 0), L(8, 3)? Both have area 6 (Diagram 2).
Equation: No: the side lengths are 3, 4, 5 and 4, √13, √13. Rigid motions keep lengths, so no sequence can carry one triangle onto the other
Return to the warm-up with the last example: equal areas are not enough. Point out that the congruence decision always rests on the definition. The side lengths only tell us that no rigid motion can work; for the "yes" case, the sequence itself is the proof.
Guided Practice15 minutes
Pairs decide whether each pair of figures is congruent, using the definition. For each "yes", they write a sequence and check it on every vertex; for each "no", they name the measurement that rigid motions would have kept:
Quadrilateral ABCD with A(1, 1), B(3, 1), C(4, 3), D(1, 3), and quadrilateral with vertices (-3, 1), (-5, 1), (-6, 3), (-3, 3). (Congruent: reflect across the line x = -1.)
The triangle with vertices (0, 0), (2, 0), (0, 2), and the triangle with vertices (5, 0), (8, 0), (5, 3). (Not congruent: the angles match, but the legs are 2 and 3 units long.)
A square with vertices (0, 0), (5, 0), (5, 5), (0, 5), and a rhombus with vertices (0, 0), (5, 0), (8, 4), (3, 4). (Not congruent: all sides are 5, but the square has 90° angles and the rhombus does not.)
Use the last pair to discuss why matching side lengths is not enough for quadrilaterals. Ask: what would a rigid motion have to do to the 90° angle of the square?
Independent Practice15 minutes
Students work alone on four tasks:
Predict the image of the line y = 2 under the 90° counterclockwise rotation about the origin, then check with two points. (The line x = -2: (0, 2) → (-2, 0) and (1, 2) → (-2, 1).)
Reflect △TUV with T(2, 1), U(5, 1), V(5, 3) across the line containing side UV. Which vertices are fixed? (U and V are fixed; T′ = (8, 1).)
Decide whether the triangle with vertices (0, 0), (3, 0), (3, 4) is congruent to the triangle with vertices (1, 5), (1, 2), (-3, 2). (Yes, sides 3, 4, 5 in both. One sequence: reflect across the line y = -x, then translate 1 unit right and 5 units up.)
Segment AB is 6 cm long with midpoint M. After any rigid motion, what can you say about M′? (M′ is the midpoint of A′B′, and A′B′ = 6 cm.)
Closure5 minutes
Exit ticket: (1) Write the definition of congruence in terms of rigid motions. (2) Two quadrilaterals have the same four side lengths, but one has an 88° angle where the other has a 90° angle. Are they congruent? Explain using what rigid motions do to angles. (3) A triangle has one vertex on line m and is reflected across m. Where does that vertex go?
Differentiation Strategies
For Struggling Students
Provide a prediction checklist to fill in before drawing: image lengths, image angles, fixed points, orientation
Let students cut out one figure and physically move it onto the other before writing the sequence in words
For congruence decisions, give a table of side lengths for both figures so students compare them first
For Advanced Students
Ask students to prove that any rigid motion takes the midpoint of a segment to the midpoint of its image
Ask for two figures with equal perimeters, equal areas and equal angle sets that are still not congruent
Ask students to show that if two figures are congruent by a sequence with two reflections, a sequence with no reflections also exists
Assessment Guidance
What to Look For
Listen for predictions that name specific measurements ("A′B′ is still 7 cm") rather than "it looks the same". For "congruent" answers, the evidence is a complete sequence with every step fully described and checked on every vertex, not a statement that the figures look alike. For "not congruent" answers, look for a specific length or angle that differs and a reason tied to the definition: rigid motions keep lengths and angles, so no sequence can exist. Equal area or equal perimeter is not evidence of congruence.
02
Classroom Activities
3 Activities
1
Predict, Then Test
20 minPairs
Each prediction card shows a figure and a rigid motion described in words. Pairs write predictions first, then carry out the motion with tracing paper and score their own predictions.
The 6 Prediction Cards
Card 1: an isosceles triangle reflected across its line of symmetry (it maps onto itself; the two base vertices swap)
Card 2: a rectangle rotated 180° about its center (it maps onto itself; opposite vertices swap)
Card 3: a segment crossing line ℓ at point X, reflected across ℓ (X stays put; the image also passes through X)
Card 4: a pair of parallel lines translated along a segment perpendicular to them (both images are parallel to the originals and to each other)
Card 5: a triangle labeled clockwise, rotated 90° about one vertex (that vertex is fixed; the labels still run clockwise)
Card 6: a trapezoid reflected across a line through none of its points (lengths and angles kept; the labels reverse direction)
Procedure
For each card, pairs write predictions about lengths, angles, fixed points, parallel lines and orientation
Pairs trace the figure and perform the motion, then mark each prediction correct or incorrect
Pairs rewrite any incorrect prediction and name the property of rigid motions it missed
Modification for Distance Learning
Share the cards as slides with a draggable, flippable copy of each figure. Pairs type predictions in a text box before moving the copy.
2
Congruent or Not? Defend It
20 minGroups of 3-4
Groups receive 8 figure-pair cards drawn on grids. For each pair they decide congruent or not congruent and write a defense based on the definition: a tested sequence for "congruent", or a measurement no rigid motion can change for "not congruent".
The 8 Figure-Pair Cards
Pair 1: two 2-by-5 rectangles, one horizontal and one vertical (congruent: a 90° rotation and a translation)
Pair 2: a 2-by-5 rectangle and a 3-by-4 rectangle (not congruent: equal perimeters, different side lengths)
Pair 3: a scalene triangle and its mirror image (congruent: a reflection)
Pair 4: two right triangles with legs 3 and 4 and legs 2 and 6 (not congruent: equal areas, different sides)
Pair 5: two circles of radius 3 with different centers (congruent: a translation)
Pair 6: a circle of radius 3 and a circle of radius 4 (not congruent: the radius is a length)
Pair 7: a regular hexagon and a copy rotated 30° about a far point (congruent: that rotation)
Pair 8: a parallelogram with sides 4 and 6 and angles 60° and 120°, and a 4-by-6 rectangle (not congruent: the angles differ)
Procedure
Each group member takes the lead on two cards and presents the defense to the group
The group must agree on every defense before moving on; a defense that says "they look the same" is sent back
Groups post one "not congruent" defense they found hardest and explain it to the class
Challenge Variation
Groups create a new pair of figures that match in area, perimeter and every angle but are not congruent, and trade it with another group.
3
Quilt Block Templates
20 minPairs
A quilter cuts triangles from printed fabric using cardboard templates. Pairs decide which pieces of a quilt block pattern can be cut with the same template, which is the same question as whether the pieces are congruent. The printed fabric adds a twist: turning a template over (a reflection) puts the print on the wrong side.
Setup
Give each pair a printed quilt block made of right triangles on a grid, with pieces numbered 1 to 8
Pairs measure the sides of each piece and group the pieces into congruence classes
Procedure
For each class, pairs write the sequence of rigid motions that carries one piece onto each of the others
Pairs mark which sequences use a reflection. Those pieces are congruent, but on one-sided printed fabric they need a flipped template
Discussion Questions
Are two pieces that need a flipped template still congruent? Why does the definition say yes?
How can you tell from the order of the vertices whether a flip is needed?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Reflecting Across the Line of a Side
Drawn to scale. △PQR reflected across the line containing side PQ (x + y = 2). P and Q lie on the line, so they are fixed; R(4, 4) goes to R′(-2, -2). The image has the same side lengths and angles, with the vertex order reversed.
Diagram 2: Equal Areas, Not Congruent
Drawn to scale. △GHI and △JKL each have a 4-unit base, a height of 3 and an area of 6 square units. Their side lengths (3, 4, 5 and 4, √13, √13) differ, so no sequence of rigid motions carries one onto the other.
04
Homework Assignment
~30 min
HSG.CO.B.6 Homework: Rigid Motions and Congruence
Directions: Use graph paper. Before drawing any image, write a prediction of its lengths, angles, fixed points and orientation. For every congruence decision, either give a sequence of rigid motions and check it on every vertex, or name a measurement that shows no sequence can exist.
Part 1: Transforming and Predicting (Problems 1-3)
Rotate △ABC with A(2, 2), B(5, 2), C(2, 6) 90° clockwise about vertex B. Give the image coordinates, and check that the side lengths 3, 4 and 5 are unchanged.
Reflect △DEF with D(1, 0), E(3, 2), F(5, 0) across the line containing side DE. Predict which vertices stay fixed, then find F′.
Square WXYZ has W(0, 0), X(6, 0), Y(6, 6), Z(0, 6). It is translated along the directed segment from W to Y. Without drawing, predict: (a) the image of W, (b) the side length of the image, (c) whether W′X′ is parallel to WX, (d) how far each point moves.
Part 2: Deciding Congruence (Problems 4-6)
Is the triangle with vertices (0, 0), (4, 0), (1, 3) congruent to the triangle with vertices (6, 1), (6, 5), (3, 2)? If so, give a sequence of rigid motions that carries the first onto the second, matched in that order.
A 4-by-6 rectangle and a 3-by-8 rectangle both have an area of 24 square units. Are they congruent? Explain using the definition of congruence in terms of rigid motions.
A tile maker has two triangular tiles, with vertices (0, 0), (6, 0), (2, 4) and (10, 0), (4, 0), (8, 4). The tiles are glazed on one side, so they can be slid and turned but not flipped over. (a) Are the tiles congruent? Give a sequence of rigid motions. (b) Can the first tile be placed exactly on the second glazed side up? Explain using orientation.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Transformations
Images correct and fully labeled
One vertex or label wrong
Images missing or incorrect
Predictions
Specific predictions of lengths, angles, fixed points and orientation, all correct
Predictions vague or partly wrong
No predictions
Congruence Decisions
Correct decision with a tested sequence or a decisive measurement
Correct decision, weak justification
Incorrect or unjustified
Use of the Definition
Reasoning cites what rigid motions preserve
Definition mentioned but not applied
Not used
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
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 statement is the definition of congruence used in high school geometry?
Answer: C
The rigid-motion definition is the one HSG.CO.B.6 uses. Choice A fails for a 2-by-6 and a 3-by-4 rectangle, which have equal areas but different side lengths. Choice B describes similarity, which allows different sizes.
Question 2 of 20 · Multiple Choice
Which property is NOT kept by every rigid motion?
Answer: D
A reflection reverses orientation, so clockwise labels become counterclockwise. Rotations and translations keep the order. Every rigid motion keeps lengths, angle measures and parallelism, so choices A, B and C are always kept.
Question 3 of 20 · Multiple Choice
Rotate the point (5, 4) 90° counterclockwise about the point A(2, 1). Where is the image?
Answer: A
Relative to A, the point is 3 right and 3 up. A 90° counterclockwise turn makes that 3 left and 3 up, so the image is (2 - 3, 1 + 3) = (-1, 4). Choice B rotates about the origin instead of A. Choice C turns clockwise. Choice D is the 180° image.
Question 4 of 20 · Multiple Choice
△PQR has P(0, 4), Q(4, 0), R(6, 5). Where does R go under the reflection across the line containing side PQ?
Answer: B
Line PQ is x + y = 4. The midpoint of R(6, 5) and (-1, -2) is (2.5, 1.5), which is on the line, and the segment has slope 1, perpendicular to the line's slope -1. Choice A reflects across y = -x, the parallel line through the origin. Choice C is that midpoint: the point where the perpendicular from R meets the line, not the image of R.
Question 5 of 20 · Multiple Choice
A triangle has an angle of 35° and its vertices are labeled clockwise. It is reflected across a line. What can you predict about the image?
Answer: C
A reflection keeps every angle measure, so the image angle is 35°, and it reverses orientation, so the labels run counterclockwise. Choice B describes a rotation or translation. Choices A and D change the angle, which no rigid motion does.
Question 6 of 20 · Multiple Choice
What is the image of the line y = x/3 + 2 under the translation 3 units right and 1 unit up?
Answer: A
The translation moves each point in the direction (3, 1), which is the direction of the line itself (slope 1/3). For example, (0, 2) goes to (3, 3), and 3/3 + 2 = 3, so the image point is on the same line. Choice B adds the vertical shift without accounting for the horizontal shift. Choice D changes the slope, and translations keep lines parallel.
Question 7 of 20 · Multiple Choice
What is the image of the line y = 2x + 1 under the rotation of 180° about the origin?
Answer: D
A 180° rotation sends (a, b) to (-a, -b): (0, 1) goes to (0, -1) and (1, 3) goes to (-1, -3). The line through these has slope 2 and y-intercept -1. The image is parallel to the original, as a 180° rotation predicts. Choice B would mean the line maps to itself, which only happens for lines through the center.
Question 8 of 20 · Multiple Choice
Is the triangle with vertices (0, 0), (3, 0), (0, 4) congruent to the triangle with vertices (2, 2), (2, 5), (6, 2), matched in that order?
Answer: A
The reflection gives (0, 0), (0, 3), (4, 0), and the translation gives (2, 2), (2, 5), (6, 2). Choice B sends (3, 0) to (5, 2), not (2, 5). Choice D forgets that a reflection is a rigid motion: reversed orientation still allows congruence.
Question 9 of 20 · Multiple Choice
One triangle has sides 5, 5 and 6. Another has sides 5, 6 and 6. Which statement is correct?
Answer: B
Any sequence of rigid motions would carry the three sides of the first triangle to three sides with the same lengths. The first triangle has two sides of 5, the second only one, so no sequence exists. Choice C is wrong because a reflection also keeps lengths.
Question 10 of 20 · Multiple Choice
Two triangles both have angles of 30°, 60° and 90°. The hypotenuse of one is 10 cm and of the other 12 cm. Are they congruent?
Answer: C
Matching angles make the triangles similar, not congruent. A rigid motion would send the 10 cm hypotenuse to a 10 cm segment, so it can never land on the 12 cm hypotenuse. Choice A confuses similarity with congruence.
Question 11 of 20 · Multiple Choice
A 3-by-5 rectangle and a 4-by-4 square both have four right angles and a perimeter of 16. Are they congruent?
Answer: D
Rigid motions keep every length, so the 5-unit side of the rectangle would have to land on a 5-unit side of the square, and the square has none. Choices A and B rely on measurements that match, but congruence needs every length and angle to match.
Question 12 of 20 · Multiple Choice
A triangle has vertex V on line m. The triangle is reflected across m. Where does V go?
Answer: B
The definition of a reflection says each point on the line of reflection is its own image, so V′ = V. Choice A describes points that are not on m.
Question 13 of 20 · Multiple Choice
△ABC is labeled clockwise and is carried onto △DEF by a sequence of rigid motions with exactly one reflection. How are D, E, F labeled?
Answer: C
Rotations and translations keep orientation, and each reflection reverses it. With exactly one reflection, the orientation is reversed once, so D, E, F run counterclockwise. Choice B is wrong because rotations never change orientation.
Question 14 of 20 · Multiple Choice
Which single rigid motion carries the segment with endpoints (1, 2) and (4, 2) onto the segment with endpoints (-2, 1) and (-2, 4), with (1, 2) going to (-2, 1)?
Answer: A
The rotation sends (1, 2) to (-2, 1) and (4, 2) to (-2, 4). Choice B sends (1, 2) to (2, 1). Choice C sends (4, 2) to (1, 1), not (-2, 4). Choice D sends (1, 2) to (2, -1).
Question 15 of 20 · Short Answer
△KLM has KL = 8, LM = 6 and m∠L = 90°. It is rotated 75° counterclockwise about M. Predict K′L′, L′M′, m∠L′ and K′M′.
K′L′ = 8, L′M′ = 6, m∠L′ = 90°, and K′M′ = 10. A rotation keeps every length and angle. KM = √(8² + 6²) = 10 by the Pythagorean theorem, so its image K′M′ is also 10. M is the center, so M′ = M.
Question 16 of 20 · Short Answer
△ABC has A(0, 0), B(2, 0), C(0, 3). Rotate it 180° about the midpoint of side AB. Give the image coordinates and describe what happens to side AB.
A′(2, 0), B′(0, 0), C′(2, -3). The midpoint of AB is (1, 0). The rotation swaps A and B, so side AB maps onto itself with its endpoints exchanged. The rest of the triangle ends up below the x-axis.
Question 17 of 20 · Short Answer
Is the triangle with vertices (1, 1), (4, 1), (4, 5) congruent to the triangle with vertices (-1, -1), (-1, -4), (-5, -4), matched in that order? Justify with the definition.
Yes. A single reflection across the line y = -x carries the first triangle onto the second: (1, 1) → (-1, -1), (4, 1) → (-1, -4), (4, 5) → (-5, -4). Both triangles have sides 3, 4 and 5, and the vertex order is reversed, which fits a sequence with one reflection.
Question 18 of 20 · Short Answer
A triangle with sides 3, 4 and 5 and an equilateral triangle with sides 4, 4 and 4 have the same perimeter. Are they congruent? Explain.
No. Both perimeters are 12, but a sequence of rigid motions would carry the 3-unit side to a 3-unit side, and the equilateral triangle has no side of length 3. Rigid motions keep lengths, so no sequence exists.
Question 19 of 20 · Short Answer
Square ABCD has A(1, 1), B(3, 1), C(3, 3), D(1, 3). Reflect it across the line containing diagonal AC. Give the image of each vertex and describe the image.
A′ = A, B′ = (1, 3) = D, C′ = C, D′ = (3, 1) = B. The line AC is y = x. A and C are on it, so they are fixed, and B and D swap. The square maps onto itself.
Question 20 of 20 · Short Answer
A shop cuts two metal brackets shaped like right triangles. Bracket 1 has vertices (0, 0), (6, 0), (0, 2) and bracket 2 has vertices (8, 5), (8, -1), (10, 5), in cm. Are the brackets congruent? Give a sequence of rigid motions if they are.
Yes. Rotate bracket 1 90° clockwise about the origin, then translate 8 cm right and 5 cm up. The rotation gives (0, 0), (0, -6), (2, 0), and the translation gives (8, 5), (8, -1), (10, 5). Both brackets have legs of 6 cm and 2 cm.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSG.CO.B.6 mean?
It means students use rigid motions to move figures, predict what a given rigid motion will do to a figure, and decide whether two figures are congruent using the rigid-motion definition: congruent figures are ones that a sequence of rotations, reflections and translations carries onto each other.
Is HSG.CO.B.6 part of Geometry?
Yes. It is a high school Geometry standard in the cluster "Understand congruence in terms of rigid motions". It usually follows the transformation standards HSG.CO.A.4 and HSG.CO.A.5 and comes before the triangle congruence criteria in HSG.CO.B.7 and HSG.CO.B.8.
Why define congruence with rigid motions instead of "same size and shape"?
Because "same size and shape" is not precise enough to check. The rigid-motion definition gives a test: find a sequence of rotations, reflections and translations that carries one figure onto the other. It works for any figure, including curves and circles, and it is the basis for the triangle congruence criteria students study next.
How do students show that two figures are NOT congruent?
They find a length or an angle that differs between the figures. Rigid motions keep every length and every angle, so if one figure has a 5-unit side and the other has none, no sequence can carry one onto the other. Equal area or equal perimeter is not enough to decide either way.
Are a figure and its mirror image congruent?
Yes. A reflection is a rigid motion, so a figure and its mirror image are congruent even though their orientation is reversed. In real life you may not be able to flip an object (a glazed tile, a printed fabric piece), but in geometry the reflection still counts.
What does "predict the effect of a rigid motion" mean in HSG.CO.B.6?
It means saying what the image will look like before drawing it: the image lengths and angles are the same, lines go to lines, parallel lines stay parallel, the center of a rotation or the points on a line of reflection stay fixed, and a reflection reverses the order of labeled vertices. Students also predict specific positions, such as where a vertex lands.
What is the difference between HSG.CO.A.5 and HSG.CO.B.6?
HSG.CO.A.5 is about drawing images and writing sequences of transformations. HSG.CO.B.6 uses that skill for a new purpose: predicting what rigid motions do and deciding congruence with the rigid-motion definition. In B.6 the sequence becomes evidence that two figures are congruent.
What mistakes do students make when deciding congruence?
Common errors include accepting equal areas or perimeters as proof, deciding from a sketch that "looks the same", testing a sequence on only one vertex, and treating mirror images as not congruent. Some students also stop after matching side lengths of quadrilaterals; a square and a rhombus with the same side length are not congruent.
How is HSG.CO.B.6 assessed?
Typical items ask students to choose the image of a figure under a described rigid motion, to predict a length, angle or orientation after a rigid motion, and to decide whether two figures are congruent with a justification: either a sequence of rigid motions or a measurement that cannot match.
What comes after HSG.CO.B.6?
Students use the rigid-motion definition to show that two triangles are congruent exactly when their corresponding sides and angles are congruent (HSG.CO.B.7), and then explain why the ASA, SAS and SSS criteria work (HSG.CO.B.8). Similarity (HSG.SRT.A.2) extends the same idea by adding dilations.
07
Related Standards
6 standards
These standards connect to HSG.CO.B.6: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
8.G.A.2Prerequisite
Understand congruence as a sequence of rotations, reflections and translations
