Determining if a Triangle is Possible

1. Determining if a Triangle is Possible Warm up Quizizz: 443303 Return to table of contents

2. How many different acute triangles can you draw? How many different right scalene triangles can you draw? Recall that triangles can be classified according to their side lengths and the measure of their angles. Sides: Scalene - no sides are congruent Isosceles - two sides are congruent Equilateral - all three sides are congruent Angles: Acute - all three angles are acute Right - contains one right angle Obtuse - contains one obtuse angle

4. Identify each pair of angles as complementary, supplementary, or neither. 1. 2. 3. 4. Find the value of x. 5. Tell whether the following statement is true or false. Angles are complementary if the sum of their measures is 180°. 6. 1 and 2 are complementary angles and m1 = 57°. What is the measure of 2? Course 2, Lesson 7-3

5. ANSWERS 1. complementary 2. supplementary 3. neither 4. x = 29 5. false 6. 33˚ Course 2, Lesson 7-3

6. How do you know if three angle measures make a triangle? Think about what relationship angles within a triangle have….

8. Decide if the following sets of angles form a triangle

9. There is another property that applies to triangles: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What does this mean? If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. If that is not true, then it is not possible to construct a triangle with the given side lengths.

10. Example 1: Determine if sides of length 5 cm, 8 cm and 12 cm can form a triangle? Test all three pairs to see if the sum is greater: 5 + 8 > 12 5 + 12 > 8 8 + 12 > 5 13 > 12 17 > 8 20 > 5 Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.

11. Example 2: Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test all three pairs to see if the sum is greater: 3 + 4 > 9 3 + 9 > 4 4 + 9 > 3 7 > 9 12 > 4 13 > 3 No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.

12. Try These: Determine if triangles can be formed with the following side lengths: 1. 4 cm, 7 cm, 10 cm 2. 24 mm, 20 mm, 30 mm 4 + 7 > 10 24 + 20 > 30 4 + 10 > 7 24 + 30 > 20 7 + 10 > 4 20 + 30 > 24 YES YES 3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in 7 + 9 = 16 9 + 13 < 24 7 + 16 > 9 9 + 24 > 13 16 + 9 > 7 13 + 24 > 9 NO NO

13. 1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work! A Yes B No

14. 2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work! A Yes B No

15. 3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work! A Yes B No

16. 4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work! A Yes B No

17. 5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work! A Yes B No

18. 6 A triangle could have which of the following sets of angles? A B C D

19. 7 A triangle could have which of the following sets of angles? A B C D

20. Classwork: Quizizz Code: 334233