Discovery Activity & Practice

Transcription

1 Discovery Activity & Practice

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5 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.

6 Students who discover a principle on their own are more capable of retaining the information.

7 Name: Classify each triangle by sides and by angles. a) 60, 60, 60 b) 45, 45, 90 c) 100, 50, 30 Give two examples of triangle classifications that are impossible. Warm-up A Name: Classify each triangle by sides and by angles. a) 60, 60, 60 b) 45, 45, 90 c) 100, 50, 30 Give two examples of triangle classifications that are impossible. Warm-up A

8 Name: Solve for x. x 32 5x 80 5x Warm-up B Name: Solve for x. x 32 5x 80 5x Warm-up B

9 Name: Solve for x. (x + 45) 2x 5x (x + 40) Warm-up B Name: Solve for x. (x + 45) 2x 5x (x + 40) Warm-up B

10 Classifying Triangles Name: Date: Class: Classify each triangle by its sides Classify each triangle by its angles Classify each triangle by its sides and by its angles 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

11 Discovering Triangle Sum Theorem Version A Name: Date: Class: Use a straightedge to draw a triangle in each box below. Make one acute triangle, one obtuse triangle, and one right triangle. A B C Use a protractor to measure each of the three angles in your triangles. Write your measurements. Triangle A Triangle B Triangle C Angle 1: Angle 1: Angle 1: Angle 2: Angle 2: Angle 2: Angle 3: Angle 3: Angle 3: 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. Copyright 2014 Math Giraffe

12 Discovering Triangle Sum Theorem Version B Name: Date: Class: Use a straightedge to draw a triangle in the box below. A Use a protractor to measure each of the three angles in your triangle. Write your measurements. Draw a different type of triangle. B 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. Copyright 2014 Math Giraffe

13 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

14 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

15 Triangle Sum Theorem Exit Ticket Name: Triangle Sum Theorem: (diagram and mathematical language) Name: Triangle Sum Theorem: (in my own words complete sentences) 2 Examples of Possible Triangles: 2 Examples of Impossible Triangles: Triangle Sum Theorem Find the missing angle measure. A triangle has angles measuring 45 degrees and 30 degrees. What is the measure of the third angle? Identify whether each set of angle measures forms a triangle. a) 62, 88, 40 b) 25, 55, 100 c) 15, 45, 75

16 Triangle Sum Theorem Name: Date: Class: Find the value for each variable. Work Answer k 2. f x 4. 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

17 Algebra Applications: Triangle Sum Theorem Name: Date: Class: 1. Solve for m. 2. Solve for c. (m + 12) (c + 1) 3c 48 2m 3. Solve for x. 4. Solve for a. 4x (3x + 5) 35 4a (a + b) Copyright 2014 Math Giraffe

18 Quiz: Classifying Triangles and Triangle Sum Theorem Name: Date: Class: Classify each triangle by both its sides and its angles Find each missing angle measure. Show all work. 7. _ m _ w 9. _ 126 x x 10. _ 41 p 87 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

19 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 x (4x + 6) 24. 5x 9x 4x 25. 4x (x + 33) Classify the triangle in #25 by its sides and angles. Copyright 2014 Math Giraffe

20 Name: Answer Key Classify each triangle by sides and by angles. a) 60, 60, 60 Equilateral, equiangular (also acute) b) 45, 45, 90 Right isosceles c) 100, 50, 30 Obtuse scalene Give two examples of triangle classifications that are impossible. Warm-up A Answers will vary. Name: Classify each triangle by sides and by angles. a) 60, 60, 60 b) 45, 45, 90 c) 100, 50, 30 Give two examples of triangle classifications that are impossible. Warm-up A

21 Name: Answer Key Solve for x. x x = x 80 x = 10 5x Warm-up B Name: Solve for x. x 32 5x 80 5x Warm-up B

22 Name: Answer Key Solve for x. (x + 45) x = 15 2x 5x (x + 40) x = 10 Warm-up B Name: Solve for x. (x + 45) 2x 5x (x + 40) Warm-up B

23 Classifying Triangles Name: Date: Class: Answer Key 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 Copyright 2014 Math Giraffe

24 Triangle Sum Theorem Exit Ticket Name: Triangle Sum Theorem: (diagram and mathematical language) Name: Answer Key Triangle Sum Theorem: (in my own words complete sentences) Answers will vary. 2 Examples of Possible Triangles: 2 Examples of Impossible Triangles: Triangle Sum Theorem Find the missing angle measure. A triangle has angles measuring 45 degrees and 30 degrees. What is the measure of the third angle? 105 degrees Identify whether each set of angle measures forms a triangle. a) 62, 88, 40 b) 25, 55, 100 c) 15, 45, 75 no yes no

25 Triangle Sum Theorem Find the value for each variable. Name: Date: Class: Answer Key Work k = 55 k Answer 2. f 115 f = x = x 4. y = 60 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 triangle has all 60 degree angles 7. A triangle with two right angles 8. a triangle with two acute angles impossible: Using Triangle Sum Theorem, there could be no third angle because the two right angles would 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. Copyright 2014 Math Giraffe

26 Algebra Applications: Triangle Sum Theorem 1. Solve for m. Name: Date: Class: 2. Solve for c. Answer Key (m + 12) (c + 1) 3c 48 2m m = 26 c = Solve for x. 4. Solve for a and b. 4x (3x + 5) 35 4a (a + b) x = 20 a = b = Copyright 2014 Math Giraffe

27 Quiz: Classifying Triangles and Triangle Sum Theorem Classify each triangle by both its sides and its angles. Name: Date: Class: Answer Key 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 = m w = 46 w 9. x = x x 10. p = p 87 Draw each triangle or explain why you are unable to. 11. Right Scalene Triangle 12. Obtuse Right Triangle Impossible: 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 Triangle Impossible: An equilateral triangle has all 60 degree angles. 14. Acute Equiangular Triangle Copyright 2014 Math Giraffe

28 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 3x (4x + 6) 24. _x = 10 5x 9x 4x 25. 4x (x + 33) x = Classify the triangle in #25 by its sides and angles. _obtuse isosceles_ Copyright 2014 Math Giraffe

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