Drawing Triangles

Examples, videos, and solutions to help Grade 7 students learn how to draw triangles under different criteria to explore which criteria result in many, a few, or one triangle.

New York State Common Core Math Grade 7, Module 6, Lesson 8

Worksheets for Grade 7

Lesson 8 Student Outcomes

• Students draw triangles under different criteria to explore which criteria result in many, a few, or one triangle.

Lesson 8 Summary

• We have seen a variety of conditions under which triangles were drawn. Our examples showed that just because a condition is given, it does not necessarily imply that the triangle you draw will be identical to another person’s drawing given those same conditions.
  
• We now want to determine exactly what conditions produce identical triangles.

Lesson 8 Classwork
Opening Exercises 1–2

1. Use your protractor and ruler to draw a right triangle DEF. Label all sides and angle measurements.
   a. Predict how many of the right triangles drawn in class are identical to the triangle you have drawn.
   b. How many of the right triangles drawn in class are identical to the triangle you drew? Were you correct in your prediction?
2. Given the following three sides of triangle ABC, use your compass to copy the triangle. The longest side has been copied for you already. Label the new triangle A’B’C’ as and indicate all side and angle measurements. For a reminder of how to begin, refer to Lesson 6, Exploratory Challenge question 10.

Exploratory Challenge
A triangle is to be drawn provided the following conditions: the measurement of two angles is 30° and 60° and the length of a side is 10 cm. Note that where each of these measurements is positioned is not fixed.
a. How is the premise of this problem different from Opening Exercise 2?
b. Do you think it will be possible to draw more than one triangle with these provided measurements so that the triangles drawn will be different from each other? Or do you think attempting to draw more than one triangle with these measurements will just keep producing the same triangle, just turned around or flipped about?
c. Based on the provided measurements, draw triangle ABC so that ∠A = 30°, ∠B = 60°, and AB = 10 cm. Describe how the 10 cm side is positioned.
d. Now, using the same measurements, draw triangle A’B’C’ so that ∠A’ = 30°, ∠B’ = 60°, and A’C’ = 10 cm.
e. Lastly, again, using the same measurements, draw triangle A’‘B’‘C’’ so that ∠A’’ = 30°, ∠B’’ = 60°, and A’‘C’’ = 10 cm.
f. Are the three drawn triangles identical? Justify your response using measurements.
g. Draw triangle A’‘‘B’‘‘C’’’ so that ∠A’’’ = 30°, ∠B’’’ = 60°, and A’‘‘C’’’ = 10 cm. Is it identical to any of the three triangles already drawn?
h. Draw another triangle that meets the criteria of this challenge. Is it possible to draw any other triangles that would be different from the three drawn above?

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