1. Common Core
7.G.2
Geometry
7th Grade

2. Common Core Standard 7.G.2 Geometry
Draw, construct, and describe geometrical figures and describe the relationships between them. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
(CCGPS) (7MA_D /MCC7.G.2

3. Directions for Teacher
The purpose of this activity is to give students an opportunity to explore the Triangle Inequality Theorem and/or Conditions of a Triangle. Students will eventually discover that the two side lengths must be greater than the third side length in order to form a triangle. This activity was done with my own students, and it was a great success! The focus of this lesson is solely on side lengths and not angle measures. An additional day is spent on angles when teaching this lesson. This is when I delve into whether or not triangles can be created, and noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Since I taught both gifted and regular 7th grade math, you can see that there is a great opportunity to extend this lesson by discussing the Triangle Inequality Theorem. It’s an easy way to amp it up without blowing their minds. Please give me feedback as to ways that the lesson can be improved upon. I hope your students enjoy it as much as mine did. As you will see, step by step instructions are given to guide students along in this activity. They are not supposed to have an answer right away, but it will come with time and with prompting from you, the teacher.

4. Conditions of a Triangle Using Side Lengths Name __________________________Class Period ________ Directions to follow for this activity: Make sure you assemble all 3 triangles prior to gluing to Sheets B and C. 1) Cut out each line segment on Sheet A. 2) Create 2 different triangles where all line segments meet. Glue the triangles to Sheet B. 3) Create a triangle where the line segments DO NOT meet to form a triangle. Glue this example to Sheet C. Example:
Student Sheet

5. Triangle #1 Triangle #2 Triangle #3
Geometry 7.G Name _______________________________________ Class Period __________
What do notice about the two shorter side lengths of triangle #1 in comparison to the longest side length?
What do notice about the two shorter side lengths of triangle #2 in comparison to the longest side length?
What observation(s) have you made about the side lengths of triangle #3 that DOES NOT meet to form a triangle? Compare the sum of the two shortest sides lengths to the longest side.
Will any combination of three side lengths create a triangle? Explain.
Can you draw a triangle with side lengths of 11 cm, 5 cm, and 6 cm?
Draw a triangle that proves the Triangle Inequality Theorem to be true. (Extension)
Triangle #1
Triangle #2
Triangle #3
The sum of the lengths of the two shortest sides
The length of the longest side of the triangle
Student Sheet

6. Cut out each line below. (These measurements are not precise, but close. )
17.5 mm
16 mm
15 mm
14 mm
13 mm
11 mm
8.5 mm
6.5 mm
4.5 mm
Sheet A

7. Triangle #1
Triangle #2
Sheet B

8. (Make sure the line segments do not meet to form a triangle)
Sheet C

9. Geometry 7.G.2 Name _______________________________________ Class Period __________
Answer Key
Table. Answers will vary.
What do notice about the two shorter side lengths of triangle #1 in comparison to the longest side length?
The sum of the two shorter sides lengths is greater than the longest side length of the triangle.
What do notice about the two shorter side lengths of triangle #2 in comparison to the longest side length?
What observation(s) have you made about the side lengths of triangle #3 that DOES NOT meet to form a triangle? Compare the sum of the two shortest sides lengths to the longest side.
The sum of the two shorter side lengths is less than the longest side length of the triangle.
The sum of the two shorter side lengths is equal to the longest side length of the triangle.
Will any combination of three side lengths create a triangle? Explain.
No, the sum of the two shorter side lengths must always be greater than the longest side length to create a triangle.
Can you draw a triangle with side lengths of 11 cm, 5 cm, and 6 cm? Not possible. 5cm + 6cm = 11 cm
Draw a triangle that proves the Triangle Inequality Theorem to be true. (Extension)
Answers will vary.

10. http://www. mathplayground. com/measuringangles. html http://www