Side Inequality Theorem
In ΔUVT, list the angles in order from longest to shortest.
UV= 17
TV=14
TU=9
∠T, ∠U, ∠V
*** 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
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
__________ = 2 congruent sides
__________ = no congruent sides
__________ = 3 congruent sides
Isosceles, Scalene, Equilateral
Using the origin as the center of the dilation, find the dilated coordinates with the given scale factor.
A(2,6) B(8,4) C(6,10)
Scale Factor = 1/2
A'(1,3) B'(4,2) C'(3,5)
In ΔSTU, list the sides in order from shortest to longest.
∠S=50°
∠T=70°
∠U=60°
UT, TS, SU
Is it possible to create a triangle with the side lengths 7, 11, 18?
No
*** The sum of all angles in a triangle equals ______.
180°
If the scale factor is less than 1, then then dilation is a _________.
Reduction
All tangent lines form a ______ angle with the radius of a circle.
Right/90°
*Daily Double*
In ΔABC, if ∠A=8x-10, ∠B=7x+6, and ∠C=7x+8, what is the longest side?
AB
The sum of the lengths of any two sides of a triangle is ________ than the length of the third side.
Greater
Find the range of possible values for the third side of a triangle with side lengths 4 and 7.
3<S<11
____________ angle = 90°
____________ angle < 90°
____________ angle >90°
Right, Acute, Obtuse
Use the equation to identify the center and radius of the circle: (x-5)2+(y+1)2 = 64
Center: (5,-1)
Radius: 8
In ΔGAB, m∠G = 35º and m∠A = 52º. Which side of the triangle is the longest side?
GA
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
In ΔGCF, list the angles in order from smallest to largest.
GC=20
CF=33
GF=19
∠C, ∠F, ∠G
True or False?
The angles within an equilateral triangle always equal 60°
True
*** List the five ways to prove that two triangles are congruent.
SAS
ASA
SSS
AAS
HL
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
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
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
*** What is the difference between congruence and similarity?
Congruence - two figures are identical in shape, proportion, angles, and size.
Similarity - two figures have the same shape, proportions, and angles, but are different sizes.
The trunk of a tree makes a 90° angle with the ground. The tree's shadow makes a 42° angle with the ground. Which of the following is true?
a. height of the tree > length of its shadow
b. height of the tree < length of its shadow
c. height of the tree = length of its shadow
b. height of the tree < length of its shadow
Side Inequality Theorem