In plain English: HSG.C.A.1 is the Common Core geometry standard that asks students to prove that any two circles are similar. The proof maps one circle onto the other with a translation that moves center onto center, then a dilation whose scale factor is the ratio of the radii. It is usually taught in high school Geometry, right after similarity transformations.
Prove that all circles are similar.
Common Core State Standards for Mathematics · Domain: Circles (C) · Cluster: Understand and apply theorems about circles Also written as HSG-C.A.1 or G-C.1 · Official standard
Students prove that any two circles are similar by using the definition of similarity from the transformations unit: two figures are similar when a sequence of rigid motions and dilations maps one onto the other. For circles, two moves are enough. A translation moves the center of the first circle onto the center of the second, and a dilation centered there, with scale factor equal to the ratio of the radii, stretches or shrinks the first circle onto the second.
The lesson insists on a complete argument. Students show that every point of the first circle lands on the second circle, and that every point of the second circle is the image of some point, so the image is the whole circle and not just part of it. Coordinate examples make each step concrete before students write the general proof with letters.
Learning Objectives
By the end of this lesson, students will be able to:
State the definition of similarity in terms of similarity transformations and apply it to circles
Describe a translation and a dilation that map a given circle onto another circle, including the translation rule and the scale factor
Track a point through the translation and the dilation and verify that its image lies on the second circle
Write a complete proof that any circle with center A and radius r is similar to any circle with center B and radius s
Use the scale factor between two circles to compare their radii, circumferences and areas
Prior Knowledge Required
Students should already be comfortable with:
Similarity as a sequence of rigid motions and dilations 8.G.A.4
Properties of dilations given by a center and a scale factor HSG.SRT.A.1
Deciding whether two figures are similar using similarity transformations HSG.SRT.A.2
The definition of a circle as the set of points at a fixed distance from a center HSG.CO.A.1
The distance formula on the coordinate plane 8.G.B.8
Post six pairs of figures and ask students to decide, without measuring, which kinds of figures are always similar to each other:
Warm-Up Prompt
"Are any two of these always similar: (1) two squares, (2) two rectangles, (3) two equilateral triangles, (4) two right triangles, (5) two regular hexagons, (6) two circles? For any 'no', sketch a pair that is not similar."
Collect votes. Squares, equilateral triangles and regular hexagons are always similar: their angles match and all their sides scale by the same factor. Rectangles and right triangles are not: a 2 by 3 rectangle and a 2 by 5 rectangle have side ratios 2/2 = 1 and 3/5, which are not equal. Nearly every student says circles are always similar, but ask how they know. "They look the same" is not a proof. Tell the class that today they will prove it with the definition of similarity.
Direct Instruction20 minutes
Definition. Two figures are similar if a sequence of rigid motions (translations, rotations, reflections) and dilations maps one figure onto the other. A circle is the set of all points at distance r from its center. Use Diagram 1 to walk through the proof with coordinates, then write the general version:
Name the circles: circle A has center A and radius r; circle B has center B and radius s, with r and s positive.
Translate: the translation along the vector from A to B moves A onto B. Translations preserve distance, so every point of circle A moves to a point at distance r from B. The image is the circle with center B and radius r.
Dilate: apply the dilation centered at B with scale factor k = s/r. A point P' at distance r from B moves along ray BP' to P'' with BP'' = k · r = (s/r) · r = s, so P'' is on circle B.
Show the image is all of circle B: for any point Q on circle B, the point on ray BQ at distance r from B is on the translated circle, and the dilation sends it to Q. So every point of circle B is an image point.
Conclude: a translation followed by a dilation maps circle A exactly onto circle B, so the circles are similar. Since the circles were arbitrary, all circles are similar.
Point out that step 4 is the step students leave out. Showing that image points land on circle B only proves the image is part of circle B. Then work through these examples, asking each time: "Where must the center go, and what scale factor do the radii give?"
Translation, then dilation
Circle A has center (6, 1) and radius 2. Circle B has center (-2, 3) and radius 5. Describe a similarity transformation that maps circle A onto circle B.
Equation: Translate by (x, y) → (x - 8, y + 2), then dilate about (-2, 3) with k = 5/2
Tracking one point
Follow the point (6, -1) on circle A from the first example through both steps.
Equation: (6, -1) → (-2, 1) → (-2, 3 + (5/2)(-2)) = (-2, -2), which is 5 units from (-2, 3)
Concentric circles
Two circles share the center (0, 0). One has radius 3 and the other has radius 7.
Equation: No translation is needed: dilate about (0, 0) with k = 7/3
Congruent circles
Two circles each have radius 4, with centers (0, 0) and (5, -2).
Equation: Translate by (x, y) → (x + 5, y - 2); the scale factor is 4/4 = 1, so the circles are congruent, a special case of similar
Scale factor from other measurements
Circle M has circumference 10π. Circle N has area 64π. Find the scale factor from M to N and the ratio of their areas.
Equation: r = 5 and s = 8, so k = 8/5 and the areas are in the ratio (8/5)² = 64/25
Use Diagram 2 to show why step 3 works for every point at once: the dilation multiplies every distance from B by k, and every point of the translated circle is exactly r from B. Mention that the order can change (dilate about A first, then translate) and that a rotation or reflection is never needed, because a circle looks the same from every direction around its center.
Guided Practice10-15 minutes
Pairs work on one pair of circles: circle C has center (1, -3) and radius 4, and circle D has center (5, 2) and radius 6. They (1) write the translation rule that moves (1, -3) onto (5, 2): (x, y) → (x + 4, y + 5); (2) find the scale factor 6/4 = 3/2; (3) track the point (5, -3) on circle C: it moves to (9, 2), then to (5 + (3/2)(4), 2) = (11, 2), which is 6 units from (5, 2); (4) explain in one sentence why every point of circle D is an image point. Circulate and listen for two errors: writing the scale factor upside down (4/6 instead of 6/4) and dilating about the origin instead of about the new center.
Independent Practice10 minutes
Students work alone on three tasks. (a) Circle E has center (0, 0) and radius 3, and circle F has center (-6, 8) and radius 12: describe a similarity transformation (translate by (x, y) → (x - 6, y + 8), then dilate about (-6, 8) with k = 4). (b) Circle G has radius 9 and circle H has radius 6: give the scale factor from G to H (2/3) and explain what a scale factor less than 1 does. (c) Write the general proof in five numbered statements, each with a reason, using the letters A, B, r and s.
Closure5 minutes
Exit ticket: "Circle J has radius 10 and circle K has radius 4. (1) What scale factor maps circle J onto circle K after the centers match? (Answer: 4/10 = 2/5.) (2) In one or two sentences, explain why the image of circle J is all of circle K and not only part of it."
Differentiation Strategies
For Struggling Students
Provide a proof frame with the five statements started and blanks for the reasons (translation preserves distance, definition of dilation, definition of circle)
Have students track three points (right, top and left of the circle) on graph paper before they write any general statement
Keep a reference card: scale factor = new radius ÷ original radius, always the image over the preimage
For Advanced Students
Show that when r ≠ s a single dilation maps circle A onto circle B, and find its center O = (B - kA)/(1 - k) for circle A with center (6, 1) and radius 2 and circle B with center (-2, 3) and radius 5
Explain why the proof never needs a rotation or a reflection, and whether the same proof works for all squares
Prove that two rectangles are similar exactly when the ratios of their side lengths match, and explain why circles need no such condition
Assessment Guidance
What to Look For
A complete proof names both transformations, gives the scale factor as s/r (image radius over original radius), and gives a reason for each step: translations preserve distance, and a dilation centered at B multiplies distances from B by k. Look for the second half of the argument, that every point of the second circle is an image point. A proof that tracks one numerical point is an example, not a proof; ask the student to repeat the argument for a point P with BP' = r.
02
Classroom Activities
3 Activities
1
Circle Pairs on Graph Paper
20 minPairs
Each pair draws two circles on graph paper, carries out the translation and the dilation by hand, and checks with a compass that the image matches the second circle. The four cards include a reduction, a concentric pair and a congruent pair, so students see that the same two-step proof covers every case.
Circle Cards
Card 1: center (2, 2), radius 1 and center (-3, 0), radius 3 (translate by (x, y) → (x - 5, y - 2), k = 3)
Card 2: center (-1, 4), radius 4 and center (3, 1), radius 2 (translate by (x, y) → (x + 4, y - 3), k = 1/2)
Card 3: center (0, -2), radius 2 and center (0, -2), radius 5 (no translation, k = 5/2)
Card 4: center (4, -1), radius 3 and center (-2, 2), radius 3 (translate by (x, y) → (x - 6, y + 3), k = 1)
Procedure
Draw both circles with a compass and label the centers and radii
Choose three points on the first circle, translate each one and draw the translated circle in a second color
Dilate the three translated points about the new center and check with the compass that each image is on the second circle
Write the translation rule and the scale factor next to the drawing
Discussion Questions
Which card needed no translation? Which needed no dilation?
Why did we dilate about the new center and not about the origin?
Three points landed on the second circle. Why is that still not a proof?
2
Always, Sometimes or Never Similar
15 minGroups of 3-4
Groups sort eight cards naming families of figures into "always similar" and "not always similar", then compare their reasons with the circle proof. The contrast shows what makes circles special: one measurement, the radius, fixes a circle's size, and nothing else about its shape can vary.
Cards
Two circles, two squares, two equilateral triangles, two regular pentagons
Two rectangles, two rhombuses, two isosceles triangles, two right triangles
Procedure
For every "not always similar" card, draw a counterexample: for instance a 4 by 6 rectangle and a 6 by 8 rectangle, whose side ratios 6/4 = 3/2 and 8/6 = 4/3 are not equal
For every "always similar" card, name the transformations that would prove it and the scale factor in terms of one measurement
Each group writes one sentence completing: "Circles are always similar because ..."
Modification for Distance Learning
Use a shared slide with draggable cards and a free dynamic geometry tool. Groups drag a dilation slider to test whether one figure can be scaled onto the other.
3
Proof Critique Gallery
20 minPairs, then whole class
Pairs write the general proof that circle A (center A, radius r) is similar to circle B (center B, radius s), then critique three flawed sample proofs posted around the room. Students learn to spot the gaps that the complete proof closes.
Flawed Sample Proofs
Proof 1: "All circles are round, so they have the same shape." (No transformation, no reasons.)
Proof 2: "Translate A to B, then dilate by r/s." (Scale factor upside down: it maps a radius r to r²/s, not to s.)
Proof 3: "Translate A to B, dilate by s/r, and the point (r, 0) lands on circle B." (Checks one point and never shows that every point of circle B is an image.)
Procedure
Pairs write their own proof first, in numbered statements with reasons
At each poster, pairs write the flaw on a sticky note and a one-line fix
The class builds one complete proof on the board from the fixes
Challenge Variation
Ask pairs to prove the same result with a single dilation when r ≠ s, by locating a center O on line AB so that the dilation about O with scale factor s/r sends A to B.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Mapping One Circle onto Another
Drawn to scale on a coordinate grid. A translation moves center A(6, 1) onto center B(-2, 3); the dashed circle is the translated copy, still with radius 2. The dilation about B with scale factor 5/2 then maps the dashed circle onto circle B. The point P(8, 1) moves to P'(0, 3) and then to P''(3, 3), which is 5 units from B.
Diagram 2: A Dilation About the Center Maps a Circle onto a Circle
Every point of the circle of radius r = 2 moves along its ray from B, and its distance from B is multiplied by k = 5/2, so it lands on the circle of radius 5. Reading the rays backward shows that every point of the larger circle comes from a point of the smaller one.
04
Homework Assignment
~30 min
HSG.C.A.1 Homework: Proving All Circles Are Similar
Directions: Show all work. When you describe a similarity transformation, give the translation rule, the center of the dilation and the scale factor. Give a reason for every step of a proof.
Part 1: Describing the Transformations (Problems 1-3)
Circle P has center (-5, 2) and radius 3. Circle Q has center (1, -1) and radius 12. Describe a translation and a dilation that map circle P onto circle Q, and state the scale factor.
Circle R has center (3, 4) and radius 5, and the point (6, 8) is on circle R. Circle T has center (-1, 0) and radius 10. Translate circle R so that its center moves onto (-1, 0), then dilate about (-1, 0). Find the image of (6, 8) after each step, and use the distance formula to show that the final image is on circle T.
Two circles share the center (0, 0): circle U has radius 8 and circle V has radius 2. Describe a single transformation that maps circle U onto circle V, give its scale factor, and explain why no translation is needed.
Part 2: Writing the Proof (Problems 4-5)
Write a complete proof that circle C, with center C and radius r, is similar to circle D, with center D and radius s. Your proof must show that every point of circle C maps to a point of circle D and that every point of circle D is the image of a point of circle C.
Circle A has circumference 18π and circle B has area 36π. Find both radii, the scale factor from circle A to circle B, and the ratio of the area of circle B to the area of circle A.
Part 3: Error Analysis (Problem 6)
A student wants to map the circle with center (2, 0) and radius 1 onto the circle with center (4, 0) and radius 3. The student writes: "Dilate about the origin with scale factor 3." Find the image of the center (2, 0) under that dilation and explain what goes wrong. Then give a correct translation and dilation. Challenge: find the center of a single dilation with scale factor 3 that does the job.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Transformations
Translation rule, dilation center and scale factor all correct
One of the three missing or incorrect
Transformations missing
Point Tracking
Images correct after each step and verified with the distance formula
Images correct but not verified
Images incorrect
Proof
Both directions shown with a reason for each step
One direction shown, or reasons missing
No general argument
Scale Factor Reasoning
Radii, scale factor and area ratio correct; error explained
Scale factor correct, ratio or explanation incomplete
Incorrect
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 similarity used to prove that all circles are similar?
Answer: C
In Common Core geometry, figures are similar when a sequence of rigid motions and dilations maps one onto the other. Choices A and B describe equal size, which similar circles usually do not have. Choice D does not apply to circles at all.
Question 2 of 20 · Multiple Choice
Circle A has center (3, -2) and radius 4. Circle B has center (-1, 5) and radius 10. Which translation moves the center of circle A onto the center of circle B?
Answer: C
Subtract the old center from the new one: -1 - 3 = -4 and 5 - (-2) = 7, so the rule is (x, y) → (x - 4, y + 7). Choice A subtracts in the wrong order and moves B toward A. Choice B uses the coordinates of the new center as the shift. Choice D adds the two centers.
Question 3 of 20 · Multiple Choice
For the circles in the previous question, what scale factor must the dilation have after the translation?
Answer: D
The scale factor is the image radius over the original radius: 10/4 = 5/2. Choice A is upside down and would shrink the circle to radius 8/5. Choice B is the difference of the radii, but a dilation multiplies distances; it does not add to them. Choice C is the product of the radii.
Question 4 of 20 · Multiple Choice
A circle of radius 6 is mapped onto a circle of radius 4 after their centers match. What is the scale factor of the dilation?
Answer: A
k = 4/6 = 2/3, a reduction, because the image is smaller. Choice B is the scale factor from the small circle to the large one. Choice C subtracts the radii, and a negative scale factor would also turn the figure around the center.
Question 5 of 20 · Multiple Choice
After a translation, circle A (radius r) has the same center B as circle B (radius s). The dilation centered at B with scale factor s/r sends a point P' with BP' = r to P''. What is BP''?
Answer: B
A dilation centered at B multiplies distances from B by the scale factor: BP'' = (s/r) · r = s, so P'' is on circle B. Choice D is the scale factor itself, not the distance. Choices A and C do not follow from the definition of a dilation.
Question 6 of 20 · Multiple Choice
Which pair of figures is ALWAYS similar?
Answer: D
Every regular octagon has eight equal sides and eight 135° angles, so a rigid motion followed by a dilation with scale factor equal to the ratio of the side lengths maps one onto the other. One measurement fixes its size, as for circles. Choice A fails because rectangles can have different length-to-width ratios. Choice B fails because rhombuses can have different angles. Choice C fails because isosceles triangles can have different vertex angles.
Question 7 of 20 · Multiple Choice
The point (4, 0) is on the circle with center (0, 0) and radius 4. What is its image under the dilation centered at (0, 0) with scale factor 3/2?
Answer: A
Multiply the distance from the center by 3/2: (3/2)(4, 0) = (6, 0), which is on the circle of radius 6. Choice B adds 3/2 instead of multiplying. Choice C divides by the scale factor. Choice D moves the point off its ray from the center.
Question 8 of 20 · Multiple Choice
Two circles share the center (2, 1). One has radius 5 and the other has radius 15. Which single transformation maps the smaller circle onto the larger one?
Answer: C
The centers already match, so only a dilation about the common center is needed, with k = 15/5 = 3. Choice D uses the wrong center: it moves (2, 1) to (6, 3), so the image circle would not be concentric. Choices A and B are rigid motions and cannot change the radius.
Question 9 of 20 · Multiple Choice
Circle F has radius 3 and circle G has radius 12. What is the ratio of the circumference of circle G to the circumference of circle F?
Answer: B
Circumference is a length, so it scales by k = 12/3 = 4: 24π ÷ 6π = 4. Choice A is k², which is the ratio of the areas. Choice D is the ratio of F to G, the reverse of what was asked.
Question 10 of 20 · Multiple Choice
A dilation with scale factor 3 maps one circle onto another. How does the area of the image compare with the area of the original circle?
Answer: D
The radius triples, so the area π(3r)² = 9πr² is 9 times as large. Choice A applies the scale factor to area as if it were a length. Choice C uses k³, which is how volumes scale.
Question 11 of 20 · Multiple Choice
A student translates circle A onto the center of circle B, dilates, and checks that one point lands on circle B. Why is this not yet a proof that the circles are similar?
Answer: B
One point is an example. The general argument shows that any point at distance r from B moves to distance s from B, and that any point of circle B comes from a point of the translated circle. Choice A is false: infinitely many circles pass through a single point. Choice C is wrong because a circle needs no rotation.
Question 12 of 20 · Multiple Choice
Two circles each have radius 7, with different centers. Which statement is true?
Answer: C
The scale factor is 7/7 = 1, so the dilation changes nothing and the translation does all the work. Congruent figures are a special case of similar figures, so choice A is false. Choice D confuses the radius with the scale factor.
Question 13 of 20 · Multiple Choice
Circle A has center (1, 2) and radius 2. Circle B has center (-3, 0) and radius 6. The point (1, 4) on circle A is translated by (x, y) → (x - 4, y - 2) and then dilated about (-3, 0) with scale factor 3. Where does it end up?
Answer: D
The translation gives (-3, 2), which is 2 units above (-3, 0). The dilation triples that distance: (-3, 0 + 3 · 2) = (-3, 6), which is 6 units from (-3, 0). Choice A stops after the translation. Choice B dilates the original point about the origin. Choice C adds 6 to the y-coordinate instead of tripling the distance from the center.
Question 14 of 20 · Multiple Choice
A single dilation with scale factor 3 maps the circle with center (0, 0) and radius 1 onto the circle with center (8, 0) and radius 3. Where is the center of that dilation?
Answer: A
The center O must satisfy O + 3((0, 0) - O) = (8, 0), so -2O = (8, 0) and O = (-4, 0). Check: (0, 0) is 4 units from (-4, 0), and (8, 0) is 12 = 3 · 4 units away on the same ray. Choice B is the midpoint of the centers, which would need a negative scale factor. Choice C would send (0, 0) to (-2, 0), and choice D would send it to (16, 0).
Question 15 of 20 · Short Answer
Circle W has center (-2, -2) and radius 3. Circle Z has center (4, 1) and radius 6. Describe a similarity transformation that maps circle W onto circle Z.
Translate by (x, y) → (x + 6, y + 3), which moves (-2, -2) onto (4, 1). Then dilate about (4, 1) with scale factor 6/3 = 2. The translation keeps the radius 3, and the dilation doubles every distance from (4, 1), so the image is circle Z.
Question 16 of 20 · Short Answer
Circle A has radius 12 and circle B has radius 20. Give the scale factor that maps circle A onto circle B and the scale factor that maps circle B onto circle A.
A onto B: 20/12 = 5/3. B onto A: 12/20 = 3/5. The two scale factors are reciprocals, because undoing a dilation divides every distance by the same factor it multiplied by.
Question 17 of 20 · Short Answer
Circle M has center (-1, 0) and radius 3, and circle N has center (2, 2) and radius 1. The point (-1, 3) is on circle M. Translate it by (x, y) → (x + 3, y + 2) and then dilate about (2, 2) with scale factor 1/3. Find its image and show that the image is on circle N.
Translation: (-1, 3) → (2, 5), which is 3 units above (2, 2). Dilation: the distance becomes 3 · (1/3) = 1, so the image is (2, 3). Its distance from (2, 2) is 1, the radius of circle N.
Question 18 of 20 · Short Answer
Explain why a dilation centered at the center of a circle maps that circle onto another circle with the same center.
Every point of the circle is r units from the center B. A dilation centered at B with scale factor k moves each point along its ray from B and multiplies its distance from B by k, so every image point is kr units from B and lies on the circle with center B and radius kr. Every point Q of that circle is reached: the point on ray BQ at distance r from B maps to Q. So the image is exactly the circle of radius kr.
Question 19 of 20 · Short Answer
Circle A has area 25π and circle B has circumference 30π. Find the scale factor from circle A to circle B and the ratio of the area of circle B to the area of circle A.
Circle A: πr² = 25π, so r = 5. Circle B: 2πs = 30π, so s = 15. The scale factor is 15/5 = 3 and the area ratio is 3² = 9 (225π ÷ 25π = 9).
Question 20 of 20 · Short Answer
A classmate writes: "Two circles are similar because they are both round." Rewrite this as a correct argument in three or four sentences.
Sample answer: Let circle A have center A and radius r and circle B have center B and radius s. Translate circle A along the vector from A to B; translations preserve distance, so the image is the circle with center B and radius r. Dilate about B with scale factor s/r; every point r units from B moves to s units from B, and every point of circle B is the image of the point r units from B on the same ray. So a translation and a dilation map circle A onto circle B, and the circles are similar.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSG.C.A.1 mean?
HSG.C.A.1 asks students to prove that all circles are similar. Students show that for any two circles, a translation and a dilation map one onto the other: the translation lines up the centers, and the dilation, with scale factor equal to the ratio of the radii, matches the sizes.
Is HSG.C.A.1 taught in Geometry or Algebra 2?
It is usually taught in high school Geometry. It sits in the circles unit and depends on the similarity transformations unit (HSG.SRT.A.1 and HSG.SRT.A.2), so it normally comes after dilations and similar triangles.
Why do students have to prove something that looks obvious?
Because "looks the same" is not a mathematical reason. The proof shows how the definition of similarity works: it asks for actual transformations, and a circle is a clean case where two of them are enough. The same reasoning later explains why arc length is proportional to the radius (HSG.C.B.5).
Which transformations are needed to show two circles are similar?
A translation and a dilation. The translation moves the center of the first circle onto the center of the second, and the dilation about that center, with scale factor s/r, changes the radius from r to s. No rotation or reflection is needed. When the radii differ, a single dilation about a well-chosen point also works.
Do concentric circles need a translation?
No. When the circles already share a center, the dilation about that center with scale factor equal to the ratio of the radii maps one onto the other on its own.
Are congruent circles similar?
Yes. Circles with equal radii are similar with scale factor 1. The dilation with scale factor 1 leaves every point where it is, so a translation alone maps one circle onto the other. Congruence is a special case of similarity.
What mistakes do students make on HSG.C.A.1 proofs?
Three errors show up often:
writing the scale factor upside down (r/s instead of s/r)
dilating about the origin instead of about the center of the second circle
showing that image points lie on the second circle but never showing that every point of the second circle is an image point
How is this standard usually assessed?
Tasks typically ask students to describe the transformations that map one given circle onto another, often with coordinates, or to complete or critique a short proof. Some tasks also ask for the ratio of circumferences or areas once the scale factor is known.
How does proving that circles are similar connect to radians?
Because all circles are similar, the arc cut off by a fixed central angle grows in proportion to the radius. The ratio of arc length to radius therefore depends only on the angle, and that ratio is the radian measure (HSG.C.B.5).
Are all squares similar too, and are all rectangles?
All squares are similar, by the same kind of argument: line up and rotate one square onto the other, then dilate by the ratio of the side lengths. Rectangles are not always similar: a 4 by 6 rectangle and a 6 by 8 rectangle have side ratios 3/2 and 4/3. Circles and squares need one measurement to fix their size; rectangles need two.
07
Related Standards
6 standards
These standards connect to HSG.C.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
8.G.A.4Prerequisite
Understand similarity as a sequence of rigid motions and dilations
