Determining if a Triangle is Possible Lesson 8.3.3 Determining if a Triangle is Possible https://www.youtube.com/watch?v=VyRf7pRe-vM

How many different acute triangles can you draw? Lesson 8.3.3 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 Cronnely

Conditions for Unique Triangles b a b AAS ASA c c two angles must sum to less than 180º two angles must sum to less than 180º a c a c b SSS SAS b two shortest sides are longer than the third side two shortest sides are longer than the third side Any set of data that fits these conditions will result in one unique triangle.

A unique triangle is a triangle that can only be drawn one way. If you are given •3 sides (SSS) eg. 5 cm, 3 cm, 7 cm •2 sides and the included angle (SAS) eg. 4 cm, 50°, 6 cm •2 angles and the side between (ASA) eg. 40°, 5 cm, 60° •1 angle and 2 sides (***) eg. 40°, 5 cm, 7 cm •A right angle, hypotenuse and another side eg. 90°, 8 cm, 3 cm

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 the two shorter sides, 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.

Yes, it is possible to construct a triangle Example 1: Determine if sides of length 5 cm, 8 cm and 12 cm can form a triangle? Are the two shorter sides (>) than the longest side? Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.

Example 2: Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Are the two shorter sides (>) than the longest side? No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.

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 YES YES 3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in 7 + 9 = 16 9 + 13 < 24 NO NO

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

Determine if sides of length 3 ft, 8 ft and 7. 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 8. Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work! Answer: B No A. Yes B. No

Determine if sides of length 5 in, 5 in and 9. 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 Answer: A Yes

10. A triangle could have which of the following sets of angles? 400, 900, 1050 350, 890, 560 750, 900, 150 300, 650, 950 Answer: B

11. A triangle could have which of the following sets of angles? 370 , 630 , 800 900 , 1040 , 760 230 , 470 , 500 800 , 900 , 100 Answer: A, D

Example 1: Predict the length of the third side of a triangle with sides of length 12 ft. and 16 ft. Side 1 = 12 ft. Side 2 = 16 ft. The 3rd side must be less than: 12 + 16 > 3rd side 28 ft > 3rd side The 3rd side must be greater than: 12 + 3rd side > 16 3rd side > 4 The 3rd side must be greater than 4 ft and less than 28 ft.

The 3rd side must be less than: 9 + 15 > 3rd side Example 2: Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm. Side 1 = 9 cm Side 2 = 15 cm The 3rd side must be less than: 9 + 15 > 3rd side 24 cm > 3rd side The 3rd side must be greater than: 9 + 3rd side > 15 3rd side > 6 The 3rd side must be greater than 6 cm & less than 24 cm.

Try These: Predict the length of the third side of a triangle whose known sides are lengths: 1. 13 mm, 20 mm 2. 7 in, 19 in 13 + 20 > Side 3 7 + 19 > Side 3 33 > Side 3 26 > Side 3 13 + Side 3 > 20 7 + Side 3 > 19 Side 3 > 7 Side 3 > 12 7 < side 3 < 33 12 < side 3 < 26

Try These: Predict the length of the third side of a triangle whose known sides are lengths: 3. 4 ft, 11 ft 4. 23 cm, 34 cm 4 + 11 > Side 3 23 + 34 > Side 3 15 > Side 3 57 > Side 3 4 + Side 3 > 11 23 + Side 3 > 34 Side 3 > 7 Side 3 > 11 7 < side 3 < 15 11 < side 3 < 57

5. Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m. 3rd < 18m 6. Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m. Answer: 18 m 3rd > 6

7. Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in. 3rd < 26 8. Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in. Answer: 26 in 3rd > 8

Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 15 ft. and 43 ft. 9. 3rd < 58 10. Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 15 ft. and 43 ft. Answer: 58 ft 3rd > 28

YES NO YES YES NO YES 8.3.3 Exit Ticket: Name __________________________________ Determine if the three sides or three angles, make a triangle. Answer yes or no. 1. 7m, 25m, 24m 4. 42 ̊, 88 ̊, 120 ̊ 2. 98 ̊, 39 ̊, 43 ̊ 5. 8ft., 10ft., 8 ft. 3. 4cm, 12cm, 7cm 6. 96 ̊, 27 ̊, 57 ̊ YES NO Answer: 58 ft YES YES NO YES

Name __________________________________ 8.3.3 Exit Ticket: Name __________________________________ Determine if the three sides or three angles, make a triangle. Answer yes or no. 1. 7m, 25m, 24m 4. 42 ̊, 88 ̊, 120 ̊ 2. 98 ̊, 39 ̊, 43 ̊ 5. 8ft., 10ft., 8 ft. 3. 4cm, 12cm, 7cm 6. 96 ̊, 27 ̊, 57 ̊ Answer: 58 ft

Name __________________________________ 8.3.3 Exit Ticket: Name __________________________________ Determine if the three sides or three angles, make a triangle. Answer yes or no. 1. 7m, 25m, 24m 4. 42 ̊, 88 ̊, 120 ̊ 2. 98 ̊, 39 ̊, 43 ̊ 5. 8ft., 10ft., 8 ft. 3. 4cm, 12cm, 7cm 6. 96 ̊, 27 ̊, 57 ̊ Answer: 58 ft

Name __________________________________ 8.3.3 Exit Ticket: Name __________________________________ Determine if the three sides or three angles, make a triangle. Answer yes or no. 1. 7m, 25m, 24m 4. 42 ̊, 88 ̊, 120 ̊ 2. 98 ̊, 39 ̊, 43 ̊ 5. 8ft., 10ft., 8 ft. 3. 4cm, 12cm, 7cm 6. 96 ̊, 27 ̊, 57 ̊ Answer: 58 ft