| Side Inequality Theorem | Triangle Inequality Theorem |
|---|---|
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∠T, ∠U, ∠V
List the angles in order from longest to shortest
UV= 17 TV=14 TU=9 |
Yes!
9+14=23 23>22
Is it possible to create a triangle with the side lengths 9, 14, 22?
14+22=36 36>9 22+9=31 31>14 |
|
UT, TS, SU
List the sides in order from shortest to longest.
∠S=50° ∠T=70° ∠U=60° |
No!
7+11=18
Is it possible to create a triangle with the side lengths 7, 11, 18?
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AB
8x-10+7x+6+7x+8=180 x=8
If ∠A=8x-10, ∠B=7x+6, and ∠C=7x+8, what is the longest side?
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Greater
The sum of the lengths of any two sides of a triangle is ________ than the length of the third side.
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GA!
35+52=87 180-87=93 93>35 93>52
In ΔGAB, m∠G = 35º and m∠A = 52º. Which side of the triangle is the longest side?
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c. {6,9,12}
6+9=15 15>12 9+12=21 21>15 12+6=18 18>9
Which set of numbers could be the side lengths of a triangle?
a. {6,9,15} b. {3,3,7} c. {6,9,12} d. {1,2,3} |
|
Angle C
4x+2+5x-3+2x+4=36 x=3
In ΔABC, AB = 4x+2, BC = 5x-3, and AC = 2x+4. The perimeter of the triangle is 36 units. Which angle in the triangle has the largest measure?
|
c. 350 feet
200+300=500 500>350 300+350=650 650>200 350+200=550 550>300
Three trees are planted. The distance from tree A to tree B is 200 feet. The distance from tree B to tree C is 300 feet. Which of the choices could be the direct distance from tree A to tree C?
a. 650 feet b. 550 feet c. 350 feet d. 50 feet |
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