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**Determining if a Triangle is Possible**

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**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

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**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.

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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.

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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.

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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

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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

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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

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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

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**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

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**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

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**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

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**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

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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.

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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