1. 01.29.2017 Format your paper for Cornell Notes. Topic: Triangles
agenda
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Cornell notes
Guided Practice
Wrap-up
Format your paper for Cornell Notes.
Topic: Triangles
E.Q. How can I determine if a triangle is possible?

2. Determining if a Triangle is Possible

3. 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. 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.

5. Example:
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 > > > 5
13 > > 8 20 > 5
Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.

6. Example:
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 > > > 3
7 > > > 3
No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.

7. 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
> > 20
> > 24
YES YES
3. 7 ft, 9 ft, 16 ft in, 13 in, 24 in
7 + 9 = < 24
> > 13
> > 9
NO NO

8. 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
Answer: B No

9. 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
Answer: A Yes

10. 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
Answer: B No

11. Determine if sides of length 3 ft, 8 ft and 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
Answer: B No

12. 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

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

14. A triangle could have which of the following sets of angles?7
A triangle could have which of the following sets of angles? A B C D
Answer: A, D

15. Example:
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.

16. Example:
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 and less than 24 cm.

17. 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

18. 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

19. 8
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: 6 m

20. 9
Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.
Answer: 18 m

21. 10
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: 8 in

22. 11
Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.
Answer: 26 in

23. 12
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: 28 ft

24. 13
Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.
Answer: 58 ft