Constructing Triangles

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Objective

SWBAT construct triangles using a compass and a straightedge

Big Idea

Students will construct triangles given segments of specific lengths.

Do Now

6 minutes

For the Do Now students will use their prior knowledge to describe the terms "scalene triangle," "isosceles triangle," and "equilateral triangle." 

 

As the students are working on the Do Now, I hand out the sheet "Constructing Triangles Mini-Lesson" and a compass and straightedge.

Mini-Lesson

15 minutes

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). 

Activity

17 minutes

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. 

Summary

7 minutes

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.