Ordering Sides and Angles
Triangle Inequality Theorem
Assorted
Definitions and Theorems
Review
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
100
Can you create a triangle with side lengths 5, 9, 11?
Yes
5+9=14 14>11
100
a) What is the Pythagorean theorem?
b) What is the hypotenuse?
a) a^2 + b^2 = c^2
b) the longest side of a right triangle, located directly opposite the right angle.
100
When the three altitudes of a triangle intersect, the intersection is called the...
orthocenter
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
What is this called: A triangle exists if the sum of the two smaller sides is larger than the third side.
Triangle Inequality Theorem.
200
When the three medians of a triangle intersect, the intersection is called the...
centroid
300
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<x<11
300
What is this called: If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and half as long.
Triangle Midsegment Theorem
300
When the three perpendicular bisectors of a triangle intersect, the intersection is called the...
circumcenter
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
400
In ΔGCF, list the angles in order from smallest to largest.
GC=20
CF=33
GF=19
∠C, ∠F, ∠G
400
a) What is an angle bisector?
b) What is a perpendicular bisector?
a) An angle bisector is a line, ray, or line segment that passes through the vertex of an angle and divides it into two equal (congruent) smaller angles.
b) A perpendicular bisector is a line, ray, or line segment that intersects another line segment at its midpoint, forming a 90-degree angle.
400
When the three angle bisectors of a triangle intersect, the intersection is called the...
incenter
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
500
In ΔABC, AB = 5 inches and BC = 3 inches. Which of the choices represents all possible values for AC, in inches?
a. 2<AC<8
b. 3≤AC≤5
c. 2in<AC<8in
d. 2in≤AC≤8in
c. 2in<AC<8in
500
Identify each center.
1. incenter.
2. orthocenter.
3. centroid.
4. circumcenter.
500
*Daily Double*
Find DE.
DE = 37