Side Inequality Theorem
Triangle Inequality Theorem
Surprise
Exterior Angle Problems
100
In ΔUVT, list the angles in order from longest to shortest.
UV= 17
TV=14
TU=9
∠T, ∠U, ∠V
100
*** Is it possible to create a triangle with the side lengths 9, 14, 22?
Yes
9+14=23 23>22
14+22=36 36>9
22+9=31 31>14
100
Can you create a triangle with side lengths 5, 9, 11?
Yes
5+9=14 14>11
9+11=20 20>5
11+5=16 16>9
100
The Exterior Angle Theorem states that the exterior angle is equal to what?
The sum of the two remote interior angles.
200
In ΔSTU, list the sides in order from shortest to longest.
∠S=50°
∠T=70°
∠U=60°
UT, TS, SU
200
Is it possible to create a triangle with the side lengths 7, 11, 18?
No
200
*** The sum of all angles in a triangle equals ______.
180°
200
Find the exterior angle when the two interior angles are 73 and 58.
131 degrees
300
*Daily Double*
In ΔABC, if ∠A=8x-10, ∠B=7x+6, and ∠C=7x+8, what is the longest side?
AB
300
The sum of the lengths of any two sides of a triangle is ________ than the length of the third side.
Greater
300
Find the range of possible values for the third side of a triangle with side lengths 4 and 7.
3<S<11
300
Solve for x.
x = 49
400
In ΔGAB, m∠G = 35º and m∠A = 52º. Which side of the triangle is the longest side?
GA
400
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}
c. {6,9,12}
6+9=15 15>12
9+12=21 21>15
12+6=18 18>9
400
In ΔGCF, list the angles in order from smallest to largest.
GC=20
CF=33
GF=19
∠C, ∠F, ∠G
400
Solve for x.
x = 12
500
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?
Angle C
500
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
c. 350 feet
200+300=500 500>350
300+350=650 650>200
350+200=550 550>300
500
In ΔABC, AB = 5 inches and BC = 3 inches. Which of the choices represents all possible values for AC, in inches?
a. 3<AC<7
b. 3≤AC≤7
c. 2<AC<8
d. 2≤AC≤8
c. 2<AC<8
500
What is the measurement of angle B?
<B = 39 degrees