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. _____________________________________________________________________ _____________________________________________________________________ 1

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 _______________________________________. 4

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. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 5

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. ______________________________________

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The angles in scalene triangles are different. ________________________________

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