DiscoveryActivity & Practice

For the inquiry activity, there are two options. Choose the 2-page version (pages 12-13) for

students who need more workspace and extra

guidance.

For “Warm-Up B,” choose the version with the star for

students who are at a higher grade level or ready for a

challenge. The equations are more difficult.

Try using only the first page of the quiz if your students are

not ready for the more challenging material.

Students who discover a

principle on their own are more

capable of retaining the information.

Classify each triangle by sides and by angles.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p A

a) 60˚, 60˚, 60˚ b) 45˚, 45˚, 90˚ c) 100˚, 50˚, 30˚

Give two examples of triangle classifications that are impossible.

Classify each triangle by sides and by angles.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p A

a) 60˚, 60˚, 60˚ b) 45˚, 45˚, 90˚ c) 100˚, 50˚, 30˚

Give two examples of triangle classifications that are impossible.

Solve for x.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

32˚

x˚

5x˚ 5x˚

80˚

Solve for x.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

32˚

x˚

5x˚ 5x˚

80˚

Solve for x.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

2x˚

(x + 45)˚

5x˚ (x + 40)˚

Solve for x.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

2x˚

(x + 45)˚

5x˚ (x + 40)˚

Classifying Triangles Name: ____________________________Date: _______________ Class: _________

Classify each triangle by its sides.1. __________ 2. __________

3. __________ 4. __________

Classify each triangle by its angles.5. __________ 6. __________

7. __________ 8. __________

Classify each triangle by its sides and by its angles.9. ___________ 10. __________

___________ __________

11. ___________ 12. _____________________ __________

Draw each triangle. Be sure to include markings for any congruent parts or right angles.13. Acute Scalene Triangle 14. Right Isosceles Triangle

15. Equiangular Triangle 16. Obtuse Isosceles Triangle

© Copyright 2014 Math Giraffe

Name: ____________________________Date: _______________ Class: _________Discovering Triangle Sum Theorem

Version AUse a straightedge to draw a triangle in each box below. Make one acute triangle, one obtuse triangle, and one right triangle.

Use a protractor to measure each of the three angles in your triangles. Write your measurements.

Find the sum of the three angle measures for triangle A. ______

Find the sum of the three angle measures for triangle B. ______

Find the sum of the three angle measures for triangle C. ______

Compare your findings. Do you notice anything significant about the sums of the angle measures for your three triangles? Write your observation in a complete sentence.__________________________________________________________________________________________________________________________________________________

Are your three sums all exactly the same? Explain why they could be similar, but not exactly the same. What could account for any slight deviations?__________________________________________________________________________________________________________________________________________________

Complete the Triangle Sum Theorem by filling in the blanks: The __________ of the measures of the three interior angles of any ___________________ is equal to _____ degrees.

A

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B C

Triangle A Triangle B Triangle C

Angle 1: Angle 1: Angle 1:

Angle 2: Angle 2: Angle 2:

Angle 3: Angle 3: Angle 3:

Name: ____________________________Date: _______________ Class: _________Discovering Triangle Sum Theorem

Version B

Use a straightedge to draw a triangle in the box below.

Use a protractor to measure each of the three angles in your triangle. Write your measurements.

__________________

Draw a different type of triangle.

Measure the angles of this triangle. Record the measures here..

__________________

Classify triangle A by its angles. ______________________

Classify triangle B by its angles. ______________________

Find the sum of the three angle measures for triangle A. ______

Find the sum of the three angle measures for triangle B. ______

A

B

© Copyright 2014 Math Giraffe

Draw one more triangle. Make sure it has a different angle classification than your first two triangles..

C

Measure the angles of this triangle. Record the measures here..

__________________

Classify triangle C by its angles. ______________

Find the sum of the three angle measures for triangle C. ______

Compare your findings. Do you notice anything significant about the sums of the angle measures for your three triangles? Write your observation in a complete sentence.__________________________________________________________________________________________________________________________________________________________________

Are your three sums all exactly the same? Explain why they could be similar, but not exactly the same. What could account for any slight deviations?__________________________________________________________________________________________________________________________________________________________________

Complete the Triangle Sum Theorem by filling in the blanks: The __________ of the measures of the three interior angles of any ___________________ is equal to _____ degrees.

© Copyright 2014 Math Giraffe

Triangle Sum Theorem Activity Name: ____________________________Date: _______________ Class: _________

Draw a large triangle on a separate sheet of paper. Cut it out and label the three interior angles A, B, and C (see figure below).

A

B

C

Rip the three points off of the triangle. Rearrange them so that their angle measures form one larger angle (see figure below).

Answer the following questions in complete sentences.1. Describe the larger angle that you have formed (type of angle and what its

measure would be).

2. What property does this illustrate? Write a rule explaining it.

© Copyright 2014 Math Giraffe

Triangle Sum Theorem:(diagram and mathematical language)

2 Examples of Impossible Triangles:

2 Examples of Possible Triangles:

Triangle Sum Theorem:(in my own words – complete sentences)

Triangle Su

m Theorem

Name:Tr

iang

le S

um

The

orem

Ex

it T

icke

t

Na

me:

Find the missing angle measure.

Identify whether each set of angle measures forms a triangle.

© Copyright 2015 Math Giraffe

© Copyright 2015 Math Giraffe

A triangle has angles measuring 45 degrees and 30 degrees. What is the measure of the third angle?

a) 62˚, 88˚, 40˚ b) 25˚, 55˚, 100˚ c) 15˚, 45˚, 75˚

Triangle Sum Theorem Name: ____________________________Date: _______________ Class: _________

Find the value for each variable.

Work Answer1.

2.

3.

4.

35˚

k˚

22˚

x˚

115˚

40˚

f˚

y˚

Draw each possible triangle. If the triangle is impossible to draw, write an explanation for why it cannot exist instead of a drawing.5. An acute scalene triangle 6. a right equilateral triangle

7. A triangle with two right angles 8. a triangle with two acute angles

9. An equilateral, equiangular triangle 10. an obtuse equilateral triangle

© Copyright 2014 Math Giraffe

Name: ____________________________Date: _______________ Class: _________

Algebra Applications:Triangle Sum Theorem

1. Solve for m. 2. Solve for c.

3. Solve for x. 4. Solve for a.

(m + 12)˚

2m˚

48˚3c˚

(c + 1)˚

35˚

4x˚

(3x + 5)˚

(a + b)˚4a˚

© Copyright 2014 Math Giraffe

Name: ____________________________Date: _______________ Class: _________

Quiz: Classifying Triangles and Triangle Sum Theorem

Classify each triangle by both its sides and its angles.

1.____________________________________

2.____________________________________

3.____________________________________

4.____________________________________

5.____________________________________

6.____________________________________

Find each missing angle measure. Show all work.

7. _____________

8. _____________

9. _____________

10. _____________

28˚

33˚

m˚

44˚

w˚

x˚ x˚

126˚

87˚41˚ p˚

Draw each triangle or explain why you are unable to.

11. Right Scalene Triangle 12. Obtuse Right Triangle

13. Obtuse Equilateral Triangle 14. Acute Equiangular Triangle

© Copyright 2014 Math Giraffe

Tell whether each statement is always, sometimes, or never true.

15. An obtuse triangle is scalene. _________________

16. A right triangle has more than one right angle. _________________

17. An equilateral triangle is acute. _________________

18. An equiangular triangle is equilateral. _________________

19. A scalene triangle has an obtuse angle. _________________

20. The measures of the angles in a triangle add up to 180 degrees. _________________

21. Two angles within a triangle have the same measure. _________________

22. An isosceles triangle has a right angle. _________________

Solve for x.

23. _________________

24. _________________

25. _________________

26. Classify the triangle in #25 by its sides and angles. _________________

(4x + 6)˚

3x˚

© Copyright 2014 Math Giraffe

5x˚

4x˚9x˚

92˚

4x˚ (x + 33)˚

Classify each triangle by sides and by angles.

Name: Answer Key

© Copyright 2015 Math Giraffe

Wa

rm-u

p A

a) 60˚, 60˚, 60˚

Equilateral, equiangular (also acute)

b) 45˚, 45˚, 90˚

Right isosceles

c) 100˚, 50˚, 30˚

Obtuse scalene

Answers will vary.

Give two examples of triangle classifications that are impossible.

Classify each triangle by sides and by angles.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p A

a) 60˚, 60˚, 60˚ b) 45˚, 45˚, 90˚ c) 100˚, 50˚, 30˚

Give two examples of triangle classifications that are impossible.

x = 58

Solve for x.

Name: Answer Key

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

x = 10

32˚

x˚

5x˚ 5x˚

80˚

Solve for x.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

32˚

x˚

5x˚ 5x˚

80˚

x = 15

Solve for x.

Name: Answer Key

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

x = 10

2x˚

(x + 45)˚

5x˚ (x + 40)˚

Solve for x.

Name:

© Copyright 2015 Math Giraffe

Wa

rm-u

p B

2x˚

(x + 45)˚

5x˚ (x + 40)˚

Classifying Triangles Name: ____________________________Date: _______________ Class: _________

Classify each triangle by its sides.1. __scalene____ 2. _equilateral__

3. __scalene___ 4. _isosceles__

Classify each triangle by its angles.5. _obtuse____ 6. ___right__

7. ___equiangular__ 8. __acute___

Classify each triangle by its sides and by its angles.9. __isosceles__ 10. ___scalene_

__obtuse___ ___right__

11. ___isosceles___ 12. __scalene_____right___ __obtuse__

Draw each triangle. Be sure to include markings for any congruent parts or right angles.13. Acute Scalene Triangle 14. Right Isosceles Triangle

15. Equiangular Triangle 16. Obtuse Isosceles Triangle

Answer Key

© Copyright 2014 Math Giraffe

Triangle Sum Theorem:(diagram and mathematical language)

2 Examples of Impossible Triangles:

2 Examples of Possible Triangles:

Triangle Sum Theorem:(in my own words – complete sentences)

Triangle Su

m Theorem

Name: Answer KeyTr

iang

le S

um

The

orem

Ex

it T

icke

t

Na

me:

Find the missing angle measure.

Identify whether each set of angle measures forms a triangle.

© Copyright 2015 Math Giraffe

© Copyright 2015 Math Giraffe

A triangle has angles measuring 45 degrees and 30 degrees. What is the measure of the third angle?

105 degrees

a) 62˚, 88˚, 40˚

no

b) 25˚, 55˚, 100˚

yes

c) 15˚, 45˚, 75˚

no

Answers will vary.

Triangle Sum Theorem Name: ____________________________Date: _______________ Class: _________

Find the value for each variable.

Work Answer1. k = 55

2. f = 25

3. x = 79

4. y = 60

35˚

k˚

22˚

x˚

115˚

40˚

f˚

y˚

Draw each possible triangle. If the triangle is impossible to draw, write an explanation for why it cannot exist instead of a drawing.5. An acute scalene triangle 6. a right equilateral triangle

impossible: An equilateral trianglehas all 60 degree angles

7. A triangle with two right angles 8. a triangle with two acute anglesimpossible: Using Triangle Sum Theorem, there could be no third angle because the two right angleswould already add up to 180 degrees.

9. An equilateral, equiangular triangle 10. an obtuse equilateral triangle impossible: An equilateral triangle has all 60 degree angles.

Answer Key

© Copyright 2014 Math Giraffe

Name: ____________________________Date: _______________ Class: _________

Algebra Applications:Triangle Sum Theorem

1. Solve for m.

m = 26

2. Solve for c.

c = 32.75

3. Solve for x.

x = 20

4. Solve for a and b.

a = 11.25b = 33.75

(m + 12)˚

2m˚

48˚3c˚

(c + 1)˚

35˚

4x˚

(3x + 5)˚

(a + b)˚4a˚

Answer Key

© Copyright 2014 Math Giraffe

Name: ____________________________Date: _______________ Class: _________

Quiz: Classifying Triangles and Triangle Sum Theorem

Classify each triangle by both its sides and its angles.

1._______scalene____________right_______

2.____isosceles_______________acute______

3.______scalene_____________obtuse_____

4.____equilateral_________equiangular____

5.____isosceles_____________obtuse______

6.______scalene_____________acute_______

Find each missing angle measure. Show all work.

7. ____m = 119__

8. ____w = 46____

9. ____x = 27_____

10. ____p = 52_____

28˚

33˚

m˚

44˚

w˚

x˚ x˚

126˚

87˚41˚ p˚

Draw each triangle or explain why you are unable to.

11. Right Scalene Triangle 12. Obtuse Right TriangleImpossible: With two angles of 90 degrees or more, there cannot be a measure for a third angle because of Triangle Sum Theorem.

13. Obtuse Equilateral TriangleImpossible: An equilateral triangle has all 60 degree angles.

14. Acute Equiangular Triangle

Answer Key

© Copyright 2014 Math Giraffe

Tell whether each statement is always, sometimes, or never true.

15. An obtuse triangle is scalene. ___sometimes____

16. A right triangle has more than one right angle. ____never________

17. An equilateral triangle is acute. ____always_______

18. An equiangular triangle is equilateral. ____always_______

19. A scalene triangle has an obtuse angle. ____sometimes____

20. The measures of the angles in a triangle add up to 180 degrees. ____always_______

21. Two angles within a triangle have the same measure. ____sometimes____

22. An isosceles triangle has a right angle. ____sometimes____

Solve for x.

23. ________x = 12____

24. _______x = 10_____

25. ______x = 11_____

26. Classify the triangle in #25 by its sides and angles. _obtuse isosceles_

(4x + 6)˚

3x˚

© Copyright 2014 Math Giraffe

5x˚

4x˚9x˚

(x + 33)˚

92˚

4x˚