Download Classifying Triangles Activity

Name ________________________ Class Period _______________ Date ________________
Classifying Triangles Activity
Objective: At the end of this task, students will know the two ways to classify triangles, name
triangles by its classification, and write the definition of triangles based on the characteristics of
the triangle.
Purpose: This activity is to be used as an introduction to Classifying Triangles. Because this
activity goes into great depth, a teacher would need to go over the answers and answer
questions from student on the topic, but I don’t think there is a need to have another class
lesson on this topic.
When finding the measures of the angles and side lengths in the triangles, make sure that the
degree measure is in units and the length measure is in tenths.
1. Open the Classifying Triangles.gsp file. Go to the “Scalene” page and follow the
instructions below and answer the questions.
a. Measure the sides of the three triangles. After measuring the lengths of each
triangle what did you notice about the measures of the sides
i. in triangle ABC? ____________________________________________________
ii. in triangle DEF? _____________________________________________________
iii. in triangle GHI? _____________________________________________________
b. In scalene triangles, the side lengths are ____________________________________.
c. A scalene triangle is classified by its _______________________________________.
d. Based off your observations made from above, write your own definition of a
Scalene Triangle.
_____________________________________________________________________
_____________________________________________________________________
e. Now measure the interior angles of the three scalene triangles. What do you notice
about the angles
i. in triangle ABC? ____________________________________________________
ii. in triangle DEF? _____________________________________________________
iii. in triangle GHI? _____________________________________________________
f. In scalene triangles the measures of the interior angles are ____________________.
g. Do the measure of the angles matter in classifying Scalene Triangles? Explain.
_____________________________________________________________________
_____________________________________________________________________
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2. Go to the “Isosceles” page. Follow the instructions below and then answer the questions.
a. Measure the sides of the three triangles. After measuring the lengths of each
triangle what did you notice about the measures of the sides
i. in triangle JKL? _____________________________________________________
ii. in triangle MNO? ____________________________________________________
iii. in triangle PQR? ____________________________________________________
b. In isosceles triangles, there are at least _______________________________ sides.
c. An isosceles triangle is classified by its _____________________________________.
d. Based off your observations made from above, write your own definition of an
Isosceles Triangle.
_____________________________________________________________________
_____________________________________________________________________
e. Now measure the interior angles of the three isosceles triangles. What do you
notice about the angles
i. in triangle JKL? _____________________________________________________
ii. in triangle MNO? ____________________________________________________
iii. in triangle PQR? ____________________________________________________
f. In isosceles triangles, there are at least _______________________________ angles.
g. Explain your answer in part 2f. Why use the term at least?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3. Go to the “Equilateral” page. Follow the instructions below and then answer the
questions.
a. Measure the sides of the three triangles. After measuring the lengths of each
triangle what did you notice about the measures of the sides
i. in triangle STU? ____________________________________________________
ii. in triangle VWX? ____________________________________________________
iii. in triangle YZA? _____________________________________________________
b. In equilateral triangles, the sides are _______________________________________.
c. An equilateral triangle is classified by its ____________________________________.
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d. Based off your observations made from above, write your own definition of an
Equilateral Triangle.
_____________________________________________________________________
_____________________________________________________________________
e. Now measure the interior angles of the three equilateral triangles. What do you
notice about the angles
i. in triangle STU? ____________________________________________________
ii. in triangle VWX? ____________________________________________________
iii. in triangle YZA? _____________________________________________________
f. What conclusion can you make about the angles in an equilateral triangle? Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
g. Based on your answer in 3f, can equilateral triangles also be isosceles triangles?
Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
4. Go to the “Acute” page. Follow the instructions below and then answer the questions.
a. Measure the angles of the three triangles. After measuring the angles of each
triangle what did you notice about the measures of the angles
i. in triangle BCD? ____________________________________________________
ii. in triangle EFG? _____________________________________________________
iii. in triangle HIJ?______________________________________________________
b. In acute triangles, the angles are __________________________________________.
c. An acute triangle is classified by its ________________________________________.
d. Based off your observations made from above, write your own definition of an Acute
Triangle.
_____________________________________________________________________
_____________________________________________________________________
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e. Do the lengths of the sides matter when classifying acute triangles? Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
5. Go to the “Right” page. Follow the instructions below and then answer the questions.
a. Measure the angles of the three triangles. After measuring the angles of each
triangle what did you notice about the measures of the angles
i. in triangle KLM? ____________________________________________________
ii. in triangle NOP? ____________________________________________________
iii. in triangle QRS? _____________________________________________________
b. In right triangles, exactly one angle measures ______________________________ .
c. A right triangle is classified by its __________________________________________.
d. Explain your answer in part 5b. Why use the term exactly?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
e. Based off your observations made from above, write your own definition of a Right
Triangle.
_____________________________________________________________________
_____________________________________________________________________
f. Do the lengths of the sides matter when classifying right triangles? Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
6. Go to the “Obtuse” page. Follow the instructions below and then answer the questions.
a. Measure the angles of the three triangles. After measuring the angles of each
triangle what did you notice about the measures of the angles
i. in triangle TUV? ____________________________________________________
ii. in triangle WXY? ____________________________________________________
iii. in triangle ZAB? _____________________________________________________
b. In obtuse triangles, exactly one angle is ___________________________________ .
c. An obtuse triangle is classified by its _______________________________________.
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d. Explain your answer in part 5b. Why use the term exactly?
_____________________________________________________________________
_____________________________________________________________________
e. Based off your observations made from above, write your own definition of a
Obtuse Triangle.
_____________________________________________________________________
_____________________________________________________________________
f. Do the lengths of the sides matter when classifying obtuse triangles? Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
7. Go to the “Equiangular” page.
questions.
Follow the instructions below and then answer the
a. Measure the angles of the three triangles. After measuring the angles of each
triangle what did you notice about the measures
i. in triangle CDE? ____________________________________________________
ii. in triangle FGH?_____________________________________________________
iii. in triangle IJK? ______________________________________________________
b. In equiangular triangles, the angles are _____________________________________.
c. An equilateral triangle is classified by its ____________________________________.
d. Based off your observations made from above, write your own definition of an
Equiangular Triangle.
_____________________________________________________________________
_____________________________________________________________________
e. Now measure the sides of the three equiangular triangles. What do you notice
about the side lengths
i. in triangle CDE? ____________________________________________________
ii. in triangle FGH?_____________________________________________________
iii. in triangle IJK? ______________________________________________________
f. What conclusion can you make about the sides in an equilateral triangle? Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
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g. Based on your answer in 3f, can equiangular triangles also be equilateral triangles?
Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
8. Triangles are classified by its ______________________ and its _______________________.
9. Go to the “Name That Triangle” page. Measure the sides and the angles of each triangle
and label the triangle according to its sides and its angles.
a. _______________________________________
b. _______________________________________
c. _______________________________________
d. _______________________________________
10. Name seven triangles according using the classification for both the sides and the angles.
a. _______________________________________
b. _______________________________________
c. _______________________________________
d. _______________________________________
e. _______________________________________
f. _______________________________________
g. _______________________________________
11. Answer each question with never, sometimes, or always.
a. Right triangles have exactly one right angle. _________________________________
b. Isosceles triangles are equilateral triangles. _________________________________
c. Equilateral triangles are isosceles triangles. _________________________________
d. Obtuse triangles have more than one obtuse angle. ___________________________
e. Equilateral triangles have the same angle measure. ___________________________
f. Equiangular triangles have the same length measure. _________________________
g. I can use the term equilateral when referring to equiangular triangles. ___________
h. Acute triangles are equiangular. __________________________________________
i.
Isosceles triangles are right triangles. ______________________________________
j.
The angles in scalene triangles are different. ________________________________
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