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| Date post: | 21-Jan-2016 |
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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?
11
16
A
B
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
A
B
C
10
12
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
2 2 229 ?20 21
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
2 2 29.8 ?3.6 7.2
96.04 12.96 51.84
+
> +
Right, Acute, or Obtuse $300
Classify the triangle by its anglesif it has sides with lengths
16, 12, 7
Right, Acute, or Obtuse $300
Acute Triangle
2 2 2( 16) ? ( 12) ( 7)
16 12 7
+
< +
Right, Acute, or Obtuse $400
Classify the triangle by its angles
if it has sides with lengths
1 1 14 , 3 , 72 3 2
Right, Acute, or Obtuse $400
Obtuse Triangle2 2 2
2 2 2
1 1 17 ? 4 32 2 3
15 9 10?
2 2 3
56.25?20.25 11.11...
56.25 31.3611...
⎛ ⎞ ⎛ ⎞ ⎛ ⎞+⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠
⎛ ⎞ ⎛ ⎞ ⎛ ⎞+⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠
+
>
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
2 2 2
7, 7, 3
7 7 3
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.
A
B
C
X - 4
x/3
50
50
Isosceles Triangles $300
AC = 2 units
Isosceles Triangles $400
Find m<C
2x X + 21D
C
E
Isosceles Triangles $400
m< C = 96 degrees
Isosceles Triangles $500
Find ZW
5a + 3
7a + 2
60
60
W
Z
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
B CD
E
Medians, Altitudes, & Bisectors $300
BE is the angle bisector.
Medians, Altitudes, & Bisectors $400
PO is the perpendicular bisector of MN.
Find ON.
O
M NP2x + 5 15 – 3x
5x + 1
Medians, Altitudes, & Bisectors $400
ON = 11 units
Medians, Altitudes, & Bisectors $500
KL is the altitude of triangle HJK.
Find the value of x.
H
K
JL
3x + 21
9x - 27
Medians, Altitudes, & Bisectors $500
9x – 27 + 3x + 21 + 90 = 180
12x + 111 = 180
12x = 96
X = 8
