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# Constructing Triangles

Lesson 6 of 13

## Objective: SWBAT construct triangles using a compass and a straightedge

*45 minutes*

#### Resources

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#### Mini-Lesson

*15 min*

After the Do Now, I instruct students to draw a long horizontal segment with one endpoint at the bottom of box 1 on the Mini-Lesson sheet. Then students "measure" the length of segment c with their compass and copy it onto the segment they drew. Make sure to have the students mark an endpoint where the arc intersects with their segment. Label this segment "d." Students then measure segment a and copy it using the left-hand endpoint of segment d. This step is repeated with segment b from the right-hand endpoint of segment d. The intersection of the two arc from segments a and b will be the third vertex of the triangle.

Students sometimes have difficulty with this construction because they draw their arcs in the wrong directions. Remind the students to make sure their arcs are drawn in the direction of the opposite endpoint and to continue for about half the circle.

In box 2, students construct a triangle using one segment for the length of the sides. The steps are the same, but students will use the same segment three times.

After both constructions are complete, I ask the students to classify each triangle and explain how they know they are correct without using a ruler (or protractor).

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#### Activity

*17 min*

In questions 1 through 6, students will practice constructing triangles like the ones from the Mini-Lesson. The constructions in questions 7 and 8 are slightly different. Students are given actual triangles to construct and not just random segments. The steps for the construction are the same, but students may have difficulty seeing how at first. As I circulate, I guide students to see how all of the constructions are similar.

As an extension, I have students construct triangles with three segments, which they draw on their own. I ask these students to investigate if it is always possible to construct triangles given any three segments and to explain why or why not. This concept, the triangle inequality theorem, will be investigated further in a later lesson.

After about 15 minutes, I show some examples of students constructions on the document camera.

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#### Summary

*7 min*

**Class Discussion:** What is the relationship between the existing triangle is question 7 and the construction? question 8?

The existing triangle and the construction are congruent. This may seem obvious, but some students may not be able to verbalize the relationship. Ask the students to explain how they know the two triangles are congruent.

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: What is Geometry?
- LESSON 2: Geometric Terms
- LESSON 3: What are Geometric Constructions?
- LESSON 4: Bisecting Angles
- LESSON 5: Constructing Parallel Lines
- LESSON 6: Constructing Triangles
- LESSON 7: Constructing Inscribed Regular Triangles, Quadrilaterals and Hexagons
- LESSON 8: Introduction to Constructions with Geometer's Sketchpad
- LESSON 9: Constructing Quadrilaterals using Geometer's Sketchpad
- LESSON 10: Constructing Regular Polygons Inscribed in Circles using Geometer's Sketchpad
- LESSON 11: Geometric Construction Review
- LESSON 12: Geometric Constructions End of Unit Assessment
- LESSON 13: Geometric Constructions Assessment Error Analysis