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Geometric Constructions
Students create exact geometric figures with compass, straightedge, paper folding, and dynamic geometry tools and explain why the methods work.
Find It. Learn It. Master It.
Beginner
15–20 minutes
Triangles & Transformations
Triangles & Transformations
Page 5 of 8
Inside Cover
Geometric Constructions
At a Glance
Binder SectionTriangles & Transformations
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How can a compass and straightedge encode geometric definitions without measuring?
Build Understanding
A geometric construction creates an exact figure using allowed tools rather than measuring and guessing. A compass transfers distances and draws arcs; an unmarked straightedge draws lines.
Core constructions include copying a segment or angle, bisecting a segment or angle, constructing perpendicular and parallel lines, and building equilateral triangles and regular polygons.
A perpendicular bisector passes through a segment's midpoint at 90 degrees. Every point on it is equidistant from the endpoints. An angle bisector divides an angle into two congruent angles.
Construction marks are evidence. Keep arcs visible and explain how equal radii or intersecting arcs guarantee the required relationship.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Copy segments and angles accurately.
- Construct segment and angle bisectors.
- Construct perpendicular and parallel lines.
- Build equilateral triangles and regular polygons.
- Explain why arc intersections establish relationships.
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Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
Construct a perpendicular bisector of AB
1
Draw equal-radius arcs from A and B that intersect above and below.
2
Connect intersections.
3
Every point on the line is equidistant from A and B.
Example 2
Bisect an angle
1
Mark equal distances on both rays, then intersect equal-radius arcs.
2
Connect the vertex to the arc intersection.
Ask and explain
Common Questions
Why not use a ruler to measure? Classical construction transfers exact relationships without numerical measurement.
Should arcs be erased? No; they show the reasoning.
What is a locus? A set of points satisfying a condition.
Can software perform constructions? Yes, when it preserves construction dependencies.
Notice and correct
Common Misconceptions
Changing compass width when equal radii are required
Lock or carefully preserve the opening.
Using visual estimation as proof
Cite equal-radius circles and congruent triangles.
Drawing arcs too small to intersect
Use a radius greater than half the segment when bisecting.
Learn Through Video
Watch, pause, and explain
Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
What tools define a classical construction?
2
We Do
Guided Practice
Construct the perpendicular bisector of segment AB. Check: arcs of equal radius intersect above and below AB.
Construct a 60-degree angle. Answer: use an equilateral triangle construction.
Copy an angle. Check: transfer one arc and its chord.
Construct a line through P parallel to line l. Check: copy a corresponding angle.
Explain why a perpendicular-bisector point is equidistant from both endpoints.
3
You Do
Independent Practice
Construct a perpendicular through a point on a line.
Construct a parallel line through an outside point.
Construct an inscribed regular hexagon.
4
Stretch Your Thinking
Challenge & Real-World Practice
Construct the circumcenter of a triangle using two perpendicular bisectors. Explain why the point is equidistant from all three vertices and test it with a circle.
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IXL
Construct a Perpendicular Bisector
Open resourceConstruct an Angle Bisector
Open resourceGeometric Constructions
Open resourceKhan Academy
Geometric Constructions
Open resourceConstructing Bisectors
Open resourceDeltaMath
DeltaMath: Segment Constructions
Open resourceDeltaMath: Angle Constructions
Open resourceDeltaMath: Parallel and Perpendicular Constructions
Open resource
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Before you begin, I can…
- I preserve required compass radii.
- I leave construction marks visible.
- I justify steps with loci, equal radii, congruence, or angle relationships.
1
Question 1
Which statement shows the key idea in this lesson?
2
Question 2
Which habit best supports accuracy?
3
Question 3
What should a student do after solving?
4
Question 4
Which explanation is strongest?
5
Question 5
How can an error be found?
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Badge EarnedGeometric Constructions Master
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