Unit 1, Lesson 4
Construction Techniques 2: Equilateral Triangles
Integrated Math 1
Preparation
Lesson Narrative
This lesson allows students to determine a process for constructing an equilateral triangle by finding the possible shapes within the construction of a regular hexagon. Students are introduced to the word inscribed to describe a situation where a polygon sits inside a circle with all the vertices on the circle. Students continue to practice straightedge and compass construction techniques and to justify claims involving distance. Students make arguments and critique the reasoning of others when discussing claims about distance using circles (MP3).
If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Constructions Tool accessible in the Math Tools or available at https://im612.org/construction-tool.
- Construct an equilateral triangle.
- Use circles in a construction to reason (using words and other representations) about lengths in figures.
- Let’s identify what shapes are possible within the construction of a regular hexagon.
- I can construct an equilateral triangle.
- I can identify congruent segments in figures and explain why they are congruent.
Required Preparation
None
inscribed
When a figure is inscribed, it is completely inside another figure so that their sides, edges, vertices, or curves touch.
- A polygon is inscribed in a circle if it fits inside the circle and every vertex of the polygon is on the circle.
- A circle is inscribed in a polygon if it fits inside the polygon and every side of the polygon is tangent to the circle.
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