Triangle
Inequality
Right,
Acute, or
Obtuse
Isosceles
Triangles
Medians,
Altitudes, &
Bisectors
$100
$100
$100
$100
$200
$200
$200
$200
$300
$300
$300
$300
$400
$400
$400
$400
$500
$500
$500
$500
Triangle Inequality $100
Can you form a triangle using the
lengths 4.8 ft, 1.3 ft, and 3.4 ft?
Why or why not?
Triangle Inequality $100
No
1.3 ft + 3.4 ft < 4.8 ft
Triangle Inequality $200
Two sides of a triangle are 6 cm & 8cm.
What can you conclude about the third
side?
Triangle Inequality $200
The third side is between 2 and 14 cm.
(12 < x < 16)
Triangle Inequality $300
In triangle ABC,
m<A = 45 degrees and m<B = 76
degrees.
Name the longest side of this triangle.
Triangle Inequality $300
AC because it is opposite <B,
which is the largest angle.
Triangle Inequality $400
What can you conclude about the
length of AB?
B
11
A
16
C
Triangle Inequality $400
AB is between 5 and 27
(5 < AB < 27)
Triangle Inequality $500
What can you conclude about the
length of AB?
m<C < m<B < m<A
B
A
12
10
C
Triangle Inequality $500
Since <C is the smallest angle,
AB is the shortest side,
therefore AB < 10,
however AB > 2 to be a triangle.
(2 < AB < 10)
Right, Acute, or Obtuse $100
Classify the triangle by its angles
if it has sides with lengths
20, 29, 21
Right, Acute, or Obtuse $100
Right Triangle
29 ?20  21
2
2
2
841  400  441
Right, Acute, or Obtuse $200
Classify the triangle by its angles
if it has sides with lengths
3.6, 7.2, 9.8
Right, Acute, or Obtuse $200
Obtuse Triangle
9.8 ?3.6  7.2
2
2
2
96.04  12.96  51.84
Right, Acute, or Obtuse $300
Classify the triangle by its angles
if it has sides with lengths
16, 12,
7
Right, Acute, or Obtuse $300
Acute Triangle
( 16) ? ( 12)  ( 7)
2
16  12  7
2
2
Right, Acute, or Obtuse $400
Classify the triangle by its angles
if it has sides with lengths
1
1
1
4 , 3 , 7
2
3
2
Right, Acute, or Obtuse $400
Obtuse Triangle
2
2
 1
 1
 1
 7  ?  4   3 
 2
 2
 3
2
2
2
 15   9 
 10 
  ?   

 2  2
 3 
56.25 ?20.25  11.11...
56.25  31.3611...
2
Right, Acute, or Obtuse $500
Two sides of a triangle measure
7 and 3.
Find a measure for the third side to make
it an acute triangle.
Right, Acute, or Obtuse $500
7, 7, 3
7  7 3
2
2
2
49  49  9
49  58
Isosceles Triangles $100
Triangle PQR is an isosceles
right triangle.
If <Q is the vertex angle,
what is the measure of <Q?
Isosceles Triangles $100
90 degrees
Isosceles Triangles $200
Triangle RST is an isosceles obtuse
triangle. If one base angle measures
32 degrees, what is the measure of
the vertex angle?
Isosceles Triangles $200
116 degrees
Isosceles Triangles $300
Find AC.
B
X-4
50
C
x/3
50
A
Isosceles Triangles $300
AC = 2 units
Isosceles Triangles $400
Find m<C
C
D
2x
X + 21
E
Isosceles Triangles $400
m< C = 96 degrees
Isosceles Triangles $500
Find ZW
W
60
5a + 3
60
Z
7a + 2
Y
Isosceles Triangles $500
ZW = 5 ½ units
Medians, Altitudes, & Bisectors
$100
What is the name of the perpendicular
segment from a vertex to the line that
contains the other side?
Medians, Altitudes, & Bisectors
$100
Altitude
Medians, Altitudes, & Bisectors
$200
What is the name of the point where all
of the medians intersect in a triangle?
Medians, Altitudes, & Bisectors
$200
The CENTROID
Medians, Altitudes, & Bisectors
$300
Name the angle bisector in the figure below.
A
E
B
D
C
Medians, Altitudes, & Bisectors
$300
BE is the angle bisector.
Medians, Altitudes, & Bisectors
$400
PO is the perpendicular bisector of MN.
Find ON.
M
2x + 5
P
15 – 3x
N
5x + 1
O
Medians, Altitudes, & Bisectors
$400
ON = 11 units
Medians, Altitudes, & Bisectors
$500
KL is the altitude of triangle HJK.
Find the value of x.
H
L
9x - 27
3x + 21
K
J
Medians, Altitudes, & Bisectors
$500
9x – 27 + 3x + 21 + 90 = 180
12x + 111 = 180
12x = 96
X=8