Determining Triangle Possibility
01.29.2017
AGENDA
Ticket in the door
Cornell notes
Guided Practice
Wrap-up
TICKET IN THE DOOR
Format your
paper for
Cornell Notes.
Topic: Triangles
E.Q. How can I
determine if a
triangle is
possible?
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Triangles can be classified by side lengths and angles. The sum of any two sides must be greater than the third for a triangle to be possible. Examples illustrate this concept with side lengths and tests to determine triangle construction possibility.
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AGENDA Ticket in the door TICKET IN THE DOOR Format your paper for Cornell Notes. Topic: Triangles E.Q. How can I determine if a triangle is possible? Cornell notes Guided Practice Wrap-up 01.29.2017
Determining if a Triangle is Possible https://www.youtube.com/watch?v=jknrgQga quM&list=PLmdFyQYShrjd51PR7FLTzUc1H_9S- a1c5 a1c5 https://www.youtube.com/watch?v=jknrgQga quM&list=PLmdFyQYShrjd51PR7FLTzUc1H_9S-
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
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.
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 > 12 5 + 12 > 8 13 > 12 17 > 8 8 + 12 > 5 20 > 5 Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.
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 > 9 3 + 9 > 4 7 > 9 12 > 4 4 + 9 > 3 13 > 3 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 4 + 10 > 7 7 + 10 > 4 YES 24 + 20 > 30 24 + 30 > 20 20 + 30 > 24 YES 3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in 7 + 9 = 16 7 + 16 > 9 16 + 9 > 7 NO 9 + 13 < 24 9 + 24 > 13 13 + 24 > 9 NO
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
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
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
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
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
6 A triangle could have which of the following sets of angles? A B C D
7 A triangle could have which of the following sets of angles? A B C D
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: 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.
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: 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 and 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
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.
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.
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.
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.
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.
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.
