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.
Lesson 8 Classwork
Opening Exercises 1–2
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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