1. Determining if a Triangle is Possible
Lesson 8.3.3
Determining if a Triangle is Possible

2. 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

3. Conditions for Unique Trianglesb 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.

4. 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

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 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.

10. 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.

11. 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.

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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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:
> 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.

19. 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:
> 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.

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

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

22. 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

23. 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

24. 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

25. 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 ̊, 88 ̊, 120 ̊
2. 98 ̊, 39 ̊, 43 ̊ ft., 10ft., 8 ft.
3. 4cm, 12cm, 7cm ̊, 27 ̊, 57 ̊
YES NO
Answer: 58 ft
YES
YES NO
YES

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

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

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