HSG.CO.A.1: Precise Definitions of Angle, Circle, Perpendicular and Parallel Lines, and Line Segment
In plain English: HSG.CO.A.1 is the Common Core geometry standard that asks students to know precise definitions of angle, circle, perpendicular line, parallel line and line segment. Each definition is built only from the undefined notions of point, line, distance along a line and distance around a circular arc. It is usually taught at the start of high school Geometry.
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Common Core State Standards for Mathematics · Domain: Congruence (CO) · Cluster: Experiment with transformations in the plane Also written as HSG-CO.A.1 or G-CO.1 · Official standard
Students learn the precise definitions that the rest of high school geometry depends on: line segment, angle, circle, perpendicular lines and parallel lines. The lesson starts from four ideas that are left undefined (point, line, distance along a line, and distance around a circular arc) and shows how each definition is built from them. Distance along a line gives the length of a segment and the meaning of "between". Distance around an arc gives the degree measure of an angle, which in turn defines a right angle and perpendicular lines.
Students test draft definitions by hunting for counterexamples, the way mathematicians do, and revise them until nothing that fits the words is the wrong kind of figure. They then use the definitions to decide whether specific points, lines and angles qualify.
Learning Objectives
By the end of this lesson, students will be able to:
Name the undefined notions (point, line, distance along a line, distance around a circular arc) and explain why geometry needs undefined terms
State precise definitions of line segment, angle, circle, perpendicular lines and parallel lines
Use distance along a line to decide whether a point lies on a segment, and distance around an arc to find an angle measure
Test a proposed definition with counterexamples and revise it until it is precise
Apply the definitions to classify figures, including lines in space that are neither parallel nor intersecting
Prior Knowledge Required
Students should already be comfortable with:
Drawing and identifying points, lines, segments, rays, angles, and perpendicular and parallel lines 4.G.A.1
Measuring an angle as a fraction of a circle, with 1 degree as 1/360 of a turn 4.MD.C.5
Distance between two numbers on a number line as the absolute value of their difference 7.NS.A.1
Finding the distance between two points in the coordinate plane with the Pythagorean Theorem 8.G.B.8
Give each student an index card. Students write their own one-sentence definition of a circle on one side, then trade cards with a partner.
Warm-Up Prompt
"Read your partner's definition of a circle. Can you draw a figure that fits every word of it but is not a circle? If you can, draw it on the back of the card."
Collect a few cards and show the counterexamples. Typical drafts are "a round shape" (an oval fits) or "a shape with no corners" (a kidney shape fits). Tell students that a precise definition leaves no room for such figures, and that today they will build five definitions this way. Ask: when you define a word you use other words, so where does the chain stop? This leads to the idea of undefined terms.
Direct Instruction20 minutes
The undefined notions. Explain that every definition uses earlier words, so geometry starts with a few terms that are described but not defined: point (a location with no size), line (straight, no thickness, extending without end in both directions), distance along a line (points on a line can be matched with numbers, like a ruler, and the distance between them is the absolute value of the difference), and distance around a circular arc (arc length). Most textbooks also leave plane undefined. Then build each definition in this order, because later ones use earlier ones:
Line segment: segment AB is the set of points A and B together with all points of line AB that lie between A and B. A point C of the line is between A and B exactly when AC + CB = AB. The length of the segment is the distance AB.
Angle: two rays with a common endpoint, called the vertex. (Ray AB is point A and every point of line AB on the same side of A as B.) The measure of an angle comes from a circle centered at the vertex: it is the fraction of the circle cut off between the rays, times 360°.
Circle: the set of all points in a plane that are a given distance (the radius) from a given point (the center). The center is not a point of the circle.
Perpendicular lines: two lines that intersect to form a right angle, an angle of 90°, whose arc is one quarter of the circle.
Parallel lines: two lines in the same plane that do not intersect.
Use Diagram 1 for the first two definitions and Diagram 2 for the last three. Work through the examples below, and ask after each one: "Which undefined notion did we just use?"
Line segment, distance along a line
On a number line, A is at -3 and B is at 9. Is C at 5 on segment AB? Is D at 12?
Equation: AC + CB = 8 + 4 = 12 = AB, so C is on AB; AD + DB = 15 + 3 = 18, so D is not
Angle measure, distance around an arc
A circle of radius 6 is centered at the vertex of an angle, and the arc between the rays has length π.
Equation: π / (2π · 6) = 1/12 of the circle, and 1/12 × 360° = 30°
Circle
A circle has center O(1, 2) and radius 5. Test P(4, 6), Q(6, 2) and R(4, 5).
Equation: OP = √(9 + 16) = 5, OQ = 5, OR = √18 ≈ 4.24, so P and Q are on the circle and R is not
Perpendicular lines
Two lines intersect, and one of the four angles they form measures 90°. Find the other three.
Equation: Each neighbor forms a linear pair with it: 180° - 90° = 90°, so all four angles are right angles
Parallel lines, counterexample
A student writes: "Parallel lines are lines that never meet." In a classroom, the line along the top of the front wall and a line along the bottom of a side wall running toward the back never meet.
Equation: Those two lines are skew, not parallel, so the definition needs "in the same plane"
After the fourth example, point out why the definition of perpendicular lines only needs one right angle: the other three follow. After the fifth, hold up a box and show the two edges. Stress that a definition must work in space, not only on the page.
Guided Practice15 minutes
Pairs test four draft definitions. For each one they either find a counterexample (a figure that fits the words but is the wrong kind of figure) or explain why none exists, then write a corrected version.
"A line segment is part of a line." (A ray is also part of a line. Fix: add the two endpoints and "all points between them".)
"A circle is all the points that are 4 cm from point O." (In space, those points form a sphere. Fix: "all points in a plane that are 4 cm from O".)
"An angle is where two lines meet." (Where two lines meet is a single point. Fix: "two rays with a common endpoint".)
"Perpendicular lines are lines that make an L." (An L can be tilted or lopsided, and "L" is not a geometric term. Fix: "two lines that intersect to form a right angle".)
Circulate and listen for students who use a term that has not been defined yet, such as "straight" for a segment or "round" for a circle. Ask them to replace it with one of the undefined notions.
Independent Practice15 minutes
Students write all five definitions from memory on a definition frame (term, definition, undefined notions used, sketch, nonexample). Then they apply them: (1) On a number line, E is at -8 and F is at 2. Is G at -3 on segment EF? Is H at 4? (EG + GF = 5 + 5 = 10 = EF, so G is on it; EH + HF = 12 + 2 = 14, so H is not.) (2) Is (6, 8) on the circle with center (0, 0) and radius 10? Is (7, 7)? (Yes: 36 + 64 = 100. No: 49 + 49 = 98, so it is just inside.) (3) A circle of radius 4 centered at an angle's vertex cuts off an arc of length 2π. Find the angle measure and decide whether the rays lie on perpendicular lines. (2π out of 8π is 1/4 of the circle, so 90°: yes.)
Closure5-10 minutes
Exit ticket: (1) Write the precise definition of parallel lines and explain why the words "in the same plane" are needed. (2) Which undefined notions does the definition of a circle use? (Point and distance, in a plane.) (3) Sketch a figure that is a ray but not a segment, and explain which part of the segment definition it fails.
Differentiation Strategies
For Struggling Students
Provide a word bank of the undefined notions and a sentence frame for each definition, such as "A ____ is the set of all points ____"
Let students test definitions with physical objects first: string for circles, a ruler edge for lines, and the corners of a box for perpendicular and parallel edges
Keep a class anchor chart with each definition, a sketch and one nonexample
For Advanced Students
Ask students to define a ray, a midpoint and a perpendicular bisector using only the five definitions and the undefined notions
Ask students to write precise definitions of a sphere and of skew lines, using only the undefined notions and the five definitions
Ask whether "two lines that form four congruent angles" is an equivalent definition of perpendicular lines, and to justify the answer with linear pairs
Assessment Guidance
What to Look For
Listen for definitions that use only undefined notions and earlier definitions, not everyday words like "round", "straight" or "corner". Strong answers include every necessary condition: both endpoints for a segment, a common endpoint for an angle, "in a plane" for a circle and for parallel lines, and a right angle (not just an intersection) for perpendicular lines. When students judge a definition, check that they give a specific counterexample instead of saying "it is too vague".
02
Classroom Activities
3 Activities
1
Counterexample Hunt
20 minGroups of 3-4
Each group receives 8 definition cards. Some are precise and some are not. For each imprecise card, the group draws a counterexample and rewrites the definition; for each precise card, it explains why no counterexample exists.
The 8 Cards
"A segment is the shortest path between two points." (Imprecise: a path is not defined yet.)
"Segment MN is M, N and every point of line MN between M and N." (Precise.)
"An angle is a figure formed by two rays that share an endpoint." (Precise.)
"An angle is a pointy shape." (Imprecise: a triangle is pointy.)
"A circle is the set of points in a plane at distance r from a point O." (Precise.)
"A circle is a figure that is the same width in every direction." (Imprecise: a rounded triangle, like some guitar picks, has constant width.)
"Perpendicular lines are a horizontal line and a vertical line." (Imprecise: turn the pair and neither line is horizontal, but they still form a right angle.)
"Parallel lines are two lines in a plane that have no point in common." (Precise.)
Procedure
Students sort the cards into "precise" and "needs work" piles and must agree on every placement
For each "needs work" card, one student draws a counterexample on the back and another writes a revised definition
Groups swap revised definitions and try to break each other's versions
Discussion Questions
Which undefined notion appears in the most precise cards?
Why can't we define "point" the same way we define "circle"?
2
String Circles and Arc Angles
20 minPairs
Students use string to act out the two distance notions. A pushpin and a fixed length of string trace a circle, and measuring string laid along an arc gives an angle measure without a protractor.
Procedure
Pin one end of a 6 cm string to the center of a cardboard square and trace the path of a pencil held at the other end. Discuss why the traced figure is exactly the set of points 6 cm from the pin
Draw two rays from the pin. Lay a second piece of string along the traced arc between the rays and measure its length
Compute the fraction of the full circle (arc length ÷ 2π(6)) and multiply by 360°. Check with a protractor
Repeat with a 10 cm string and the same two rays. The arc is longer but the fraction, and therefore the angle, is the same
Discussion Questions
Why does an angle's measure not depend on which circle we use?
Which ray drawing gives an arc of exactly one quarter of the circle? What name do we give the lines those rays lie on?
Modification for Distance Learning
Students use a phone or laptop screen with dynamic geometry software: construct a circle by center and radius, place two rays and measure the arc length. They share a screenshot of both circles with the same angle.
3
Parallel, Perpendicular or Skew?
15 minPairs
Students treat a shoebox (or the classroom itself) as a model of space and classify pairs of edge lines, using the definitions word by word.
Setup
Label the top corners of the box A, B, C, D and the corners directly below them E, F, G, H, so that E is under A, F under B, G under C and H under D.
Procedure
Each pair lists 6 pairs of edge lines: 2 parallel, 2 perpendicular and 2 that neither intersect nor are parallel
For every pair, students write which words of the definition it meets and which it fails, for example "no common point, but not in one plane"
Students check right angles with the corner of an index card
Challenge Variation
Ask: can two lines be perpendicular to the same line and still not be parallel to each other? Students look for an example on the box (they can: two edges at one corner are both perpendicular to the vertical edge there).
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Segment and Angle from the Undefined Notions
Left: on a number line, C lies on segment AB because AC + CB = AB, while D lies on line AB but outside the segment. Right: the 30° angle is drawn to scale; its measure comes from the fraction of a circle centered at the vertex V that lies between the rays.
Diagram 2: Circle, Perpendicular Lines and Parallel Lines
The circle is drawn to scale on a grid: P and Q are exactly 5 units from the center, R is not. Perpendicular lines ℓ and m meet at a right angle, which forces all four angles to be 90°. Parallel lines j and k lie in one plane and share no point.
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Homework Assignment
~30 min
HSG.CO.A.1 Homework: Precise Geometry Definitions
Directions: Show your work. When you use a definition, write it out and underline the undefined notions it uses. When you reject a statement, give a specific counterexample with a sketch.
Part 1: Segments, Angles and Circles (Problems 1-3)
On a number line, J is at -5 and K is at 7. (a) Find the length of segment JK. (b) Use the betweenness test (JM + MK = JK) to decide whether M at 2 and N at 9 lie on segment JK. (c) Explain why N still lies on line JK.
Two rays share the endpoint V. A circle of radius 8 centered at V cuts off an arc of length 2π between the rays. (a) Find the angle measure. (b) What arc length would a circle of radius 3 centered at V cut off between the same rays? (c) Explain why the angle measure does not depend on the circle.
A circle has center C(-1, 3) and radius 10. For each point, decide whether it is on, inside or outside the circle, and justify with the distance from C: P(5, 11), Q(7, -2), R(-9, 10).
Part 2: Perpendicular and Parallel Lines (Problems 4-6)
Lines r and s intersect, and one of the angles they form measures 88°. (a) Find the other three angles. (b) Are r and s perpendicular? Use the definition. (c) Explain why, for perpendicular lines, knowing that one angle is 90° is enough.
A shoebox has top corners A, B, C, D and bottom corners E, F, G, H, with E below A, F below B, G below C and H below D. Using lines through the edges, name (a) two lines that are parallel, (b) two lines that are perpendicular, and (c) two lines that do not intersect and are not parallel. For (c), explain which part of the definition of parallel lines fails.
Write precise definitions of line segment, angle, circle, perpendicular lines and parallel lines, and underline the undefined notions in each. Then give a counterexample to the statement "A circle is a figure in a plane whose points are all the same distance from one point."
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Precise Definitions
All five correct, with every necessary condition
Mostly correct, one condition missing
Everyday words or missing conditions
Undefined Notions
Correctly identified in each definition
Identified in some definitions
Not identified
Using Distance
Betweenness, arc and circle tests set up and computed correctly
Correct setup with an arithmetic error
Tests missing or incorrect
Counterexamples
Specific, sketched and explained
Given but not explained
Missing
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Choose an answer for each multiple-choice question to see whether it is right and why. Write the short answers on paper before opening the answer. Reset quiz clears all answers.
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 is a precise definition of a circle?
Answer: B
Choice B uses only a point, a distance and a plane, and no other figure fits it. Choice A fits an oval. Choice C describes a disk (the inside region), not the circle itself. Choice D fits a rounded triangle of constant width, the shape of some guitar picks.
Question 2 of 20 · Multiple Choice
On a number line, A is at -6 and B is at 4. Which point lies on segment AB?
Answer: C
AB = 10. For the point at -1, the distances to A and B are 5 and 5, and 5 + 5 = 10, so it is between A and B. For -8 the distances add to 2 + 12 = 14, and for 5 they add to 11 + 1 = 12, so those points are on line AB but outside the segment. A common error is to think any point near A or B counts.
Question 3 of 20 · Multiple Choice
Which is a precise definition of an angle?
Answer: A
An angle is two rays with a common endpoint, the vertex. Choice B describes intersecting lines, which form four angles. Choice C leaves out angles that are not in polygons. Choice D confuses the angle with its measure.
Question 4 of 20 · Multiple Choice
Which is a precise definition of parallel lines?
Answer: D
Choice D is the definition. Choice A uses "direction", which is not defined. Choice B fails because two segments can miss each other and still lie on lines that cross. Choice C is too narrow: slanted lines can be parallel.
Question 5 of 20 · Multiple Choice
Lines p and q intersect, and one of the angles they form measures (3x + 15)°. For which value of x are p and q perpendicular?
Answer: A
Perpendicular lines are lines that intersect to form a right angle, so 3x + 15 = 90, 3x = 75 and x = 25. One right angle is enough, because the other three angles then follow. Choice B drops the 15 and solves 3x = 90. Choice C sets the angle equal to 180°, a straight angle, not a right angle. Choice D adds 15 to 90 instead of subtracting it (3x = 105).
Question 6 of 20 · Multiple Choice
A circle of radius 9 is centered at the vertex of an angle. The arc between the rays has length 3π. What is the angle measure?
Answer: B
The circumference is 2π(9) = 18π, and 3π/18π = 1/6. One sixth of 360° is 60°. Choice C uses πr = 9π instead of 2πr. Choice A uses the diameter 18 as the radius. Choice D confuses the arc length 3π ≈ 9.4 with the angle measure.
Question 7 of 20 · Multiple Choice
A circle has center (2, -1) and radius 5. Which point is on the circle?
Answer: D
The distance from (2, -1) to (5, 3) is √(3² + 4²) = √25 = 5. For (4, 3) the distance is √20, for (7, 0) it is √26, and for (-1, -4) it is √18, so none of those is exactly 5.
Question 8 of 20 · Multiple Choice
Which of these is one of the undefined notions that HSG.CO.A.1 builds the definitions on?
Answer: C
Point is undefined, along with line, distance along a line and distance around a circular arc. Angle, circle and line segment are the terms students define from those notions.
Question 9 of 20 · Multiple Choice
On a number line, A is at -9 and B is at 4. What is the length of segment AB?
Answer: A
Distance along a line is the absolute value of the difference: |4 - (-9)| = 13. Choice B gives a negative length (-9 - 4), which is impossible for a distance. Choice D adds the coordinates instead of subtracting them (-9 + 4 = -5), and choice C drops the sign of -9 (9 - 4 = 5).
Question 10 of 20 · Multiple Choice
Which figure shows that "Perpendicular lines are lines that intersect" is not a precise definition?
Answer: B
Lines meeting at 50° fit the draft definition but are not perpendicular, so they are a counterexample. The definition must say the lines form a right angle. Choice A fits both the draft and the correct definition, so it proves nothing.
Question 11 of 20 · Multiple Choice
In a rectangular room, consider the line where the ceiling meets the front wall and the line where the floor meets the back wall. Both run from left to right. Are they parallel?
Answer: B
A slanted plane, like a sheet of plywood leaned from the top of the front wall to the bottom of the back wall, contains both lines, and they never meet, so they fit the definition exactly. Choices A and D add conditions the definition does not have. Choice C is wrong because skew lines are lines that no single plane contains.
Question 12 of 20 · Multiple Choice
Points A, B and C lie on one line with AC = 7, AB = 11 and CB = 18. Which point is between the other two?
Answer: A
Test each point with the betweenness condition. CA + AB = 7 + 11 = 18 = CB, so A is between C and B. C is not between A and B because AC + CB = 25, not 11. A common error is to assume the middle letter of the name is between the others.
Question 13 of 20 · Multiple Choice
Is the center of a circle a point of the circle?
Answer: D
The circle is only the points at the given distance r from the center, and the center is 0 units from itself. Choices A and B confuse the circle with the disk it encloses. Choice C is false: the center lies in the plane of the circle.
Question 14 of 20 · Multiple Choice
Two circles, of radius 2 and radius 5, are centered at the vertex of the same angle. The arcs between the rays have lengths 2π/3 and 5π/3. What is the angle measure?
Answer: A
Small circle: (2π/3) ÷ (4π) = 1/6. Large circle: (5π/3) ÷ (10π) = 1/6. Both give 1/6 × 360° = 60°. The arc length grows with the radius, but the fraction of the circle stays the same, so the angle measure does not depend on the circle. Choice B divides 5π/3 by 4π instead of 10π.
Question 15 of 20 · Short Answer
Write a precise definition of perpendicular lines. Then explain why it is enough for the definition to require only one right angle.
Perpendicular lines are two lines that intersect to form a right angle (an angle of 90°). Two intersecting lines form four angles. Each angle next to the right angle forms a linear pair with it, so it measures 180° - 90° = 90°, and the angle opposite is 90° as well. One right angle therefore forces all four.
Question 16 of 20 · Short Answer
Define segment PQ using the idea of "between". On a number line, P is at -2 and Q is at 10. Which of the points -4, 0, 6, 10 and 11 lie on segment PQ?
Segment PQ is P, Q and every point X of line PQ with PX + XQ = PQ. Here PQ = 12. 0, 6 and 10 are on the segment (2 + 10, 8 + 4 and 12 + 0 all equal 12). -4 gives 2 + 14 = 16 and 11 gives 13 + 1 = 14, so they are on the line but not on the segment.
Question 17 of 20 · Short Answer
A student says: "Parallel lines are lines that stay the same distance apart." Explain why the definition "two lines in the same plane that do not intersect" is preferred at the start of geometry.
The precise definition uses only undefined notions and the idea of intersecting. "The distance between two lines" is not an undefined notion: to measure it you need perpendicular segments, so the student's version depends on ideas that come later. That parallel lines stay the same distance apart is a property that is proved later (with the parallel postulate), not the definition.
Question 18 of 20 · Short Answer
A circle has center (0, 0) and radius 13. Find two points with integer coordinates in different quadrants that are on the circle, and one point with integer coordinates that is not. Justify each with the definition.
Sample answer: (5, 12) and (-12, 5) are on the circle because 5² + 12² = 169 = 13², so each is exactly 13 units from the center. (10, 10) is not, because 10² + 10² = 200 and √200 ≈ 14.1, not 13. Other correct points include (12, -5) and (-5, -12).
Question 19 of 20 · Short Answer
A circle of radius 5 is centered at the vertex of an angle, and the arc between the rays has length 7π/3. Find the angle measure. Are the lines containing the rays perpendicular?
The circumference is 10π, and (7π/3) ÷ 10π = 7/30. Then 7/30 of 360° is 84°. No: perpendicular lines must form a right angle, and these lines form angles of 84° and 96°, so none of the four angles is 90°.
Question 20 of 20 · Short Answer
List the undefined notions HSG.CO.A.1 uses. Then write the definition of an angle and of a circle, and name the undefined notions each one relies on.
Undefined notions: point, line, distance along a line and distance around a circular arc (many texts add plane). An angle is two rays with a common endpoint; it relies on point and line (a ray is part of a line), and its measure relies on distance around a circular arc. A circle is the set of all points in a plane at a given distance from a given point; it relies on point and distance (and plane).
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSG.CO.A.1 mean?
HSG.CO.A.1 means students must know exact definitions of angle, circle, perpendicular line, parallel line and line segment. The standard also says what those definitions rest on: point, line, distance along a line and distance around a circular arc, which are left undefined. "Know" here means being able to state the definition, apply it to a figure and explain why a vague version fails.
Why are point and line undefined in geometry?
Because every definition uses other words, the chain has to start somewhere. Geometry starts with a few terms that are described and used but not defined, much as a dictionary would go in circles if it tried to define every word. Everything else, including the five terms in this standard, is defined from them.
Is HSG.CO.A.1 taught in Geometry or Algebra 1?
It is usually taught in high school Geometry, often in the first unit. Students met the same terms informally in grade 4 (4.G.A.1), where they drew and identified them. HSG.CO.A.1 asks for precise definitions that can be used in proofs.
What does "distance around a circular arc" have to do with angles?
It gives angles their measure. Draw a circle centered at the vertex: the arc between the rays is some fraction of the circle, and the angle measure is that fraction of 360°. The fraction is the same for every circle centered at the vertex, so the measure depends only on the angle. This is also why a right angle is one quarter of a full turn.
What is a common mistake with the definition of a circle?
Leaving out "in a plane". The set of all points at a given distance from a given point in space is a sphere. A second common mistake is to think the center belongs to the circle: it does not, because it is 0 units from itself, not r units.
Why do parallel lines have to be in the same plane?
Because without that condition, skew lines would count as parallel. Two edges of a box, such as a top edge of the front face and a bottom edge of a side face running toward the back, never meet, yet they point in different directions. Such lines are called skew.
What is the difference between a line, a segment and a ray?
A line extends without end in both directions, a segment has two endpoints, and a ray has one endpoint and extends without end in one direction. Segment AB contains A, B and every point of line AB between them. Ray AB starts at A, passes through B and keeps going.
How is HSG.CO.A.1 tested?
Usually through items that ask students to choose or complete a precise definition, find the flaw in a vague one, or use a definition to justify a step. Later geometry tasks test it indirectly: every proof about perpendicular or parallel lines, and every definition of a rotation or reflection in HSG.CO.A.4, relies on these definitions.
How can parents help with this standard at home?
Play the counterexample game. Ask your student for a definition, such as "What is a circle?", and then try to draw a shape that fits their words but is the wrong figure. Everyday objects help too: the edges of a cereal box show parallel, perpendicular and skew lines.
What comes after HSG.CO.A.1?
Students use these definitions to define rotations, reflections and translations (HSG.CO.A.4) and then to prove theorems about lines and angles (HSG.CO.C.9). For example, a reflection is defined using perpendicular lines and segments, and a rotation uses circles and angles.
07
Related Standards
5 standards
These standards connect to HSG.CO.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
4.G.A.1Prerequisite
Draw points, lines, segments, rays, angles, and perpendicular and parallel lines
Lesson coming soon
4.MD.C.5Prerequisite
Understand angle measure as a fraction of a circle, with 1 degree as 1/360 of a turn
Lesson coming soon
Alongside
HSG.CO.A.2Parallel
Represent transformations as functions and compare rigid and non-rigid ones
