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Transcript
Aim: What is an Isosceles Triangle?
Do Now:
What type of triangle has sides of 3, 6, 8?
Aim: Isosceles Triangle
Course: Applied Geometry
Triangles
A triangle is a three sided polygon enclosing three
angles.
The sum of the measure of the angles of a triangle
is 180 degrees (1800)
3 equal
sides
2 equal
sides
Aim: Isosceles Triangle
No equal
sides
Course: Applied Geometry
Isosceles Triangle
Isosceles Triangle
A triangle with two sides that are
equal in length.
AB  BC
B
leg
A
leg
Base angles
Base
C
Base angles of an isosceles triangle
are congruent Course: Applied Geometry
Aim: Isosceles Triangle
The Special Lines of a Triangle
Altitude
BH is an altitude from B to AC
Altitude of a Triangle - A line segment from a
vertex and perpendicular to the opposite side.
Angle Bisector
BQ is the bisector of  B:
mABQ = mCBQ
Angle bisector of a triangle - A line segment that
divides an angle
a triangle
into Course:
twoApplied
halves.
Aim: of
Isosceles
Triangle
Geometry
Median
BM is the median from B to the midpoint of AC: AM = MC
Median of a triangle - A line segment from a
vertex of a triangle to the midpoint of the
opposite side.
Special lines of
various triangles
Aim: Isosceles Triangle
Course: Applied Geometry
Special Lines of an Isosceles Triangle
Altitude - line segment from
a vertex and perpendicular to
the opposite side.
F
E
H
Angle bisector - A line
segment that divides an angle
of a triangle into two halves.
G
Median - A line segment
from a vertex to the
midpoint of the opposite
side.
In an isosceles triangle, all of three of these lines,
drawn from the vertex angle, are the same line.
Aim: Isosceles Triangle
Course: Applied Geometry
Model Problem
I
Complete each statement. Explain.
a. KI  _____ b. KN  ____
N
c . ML  _____
K
L
M
J
Aim: Isosceles Triangle
Course: Applied Geometry
Model Problem
Find the measure of the vertex angle of an
isosceles triangle if a base angle measures:
A. 44o
180o - (44o + 44o)
180o - (88o) = 92o
92o
44o
44o
Find the measure of the base angles of an
isosceles triangle if the vertex angle measures:
B. 44o
44o
180o - 44o = 136o
2x = 136o
x = 68o
o o
x68
Aim: Isosceles Triangle
68xoo
Course: Applied Geometry
Model Problem
B
Triangle ABC is
isosceles with AB  BC,
AB = 3x - 2 and BC =
5x – 14. Find the value
of x:
16
16
C
A
3x - 2 = 5x - 14
-3x
-3x
- 2 = 2x - 14
+14
+14
+12 = 2x
6=x
Aim: Isosceles Triangle
3x - 2
3(6) - 2= 16
5x - 14
5(6) - 14= 16
Course: Applied Geometry
Model Problem
The measure of the vertex angle of an
isosceles triangle is 100o. Find the number
of degrees in one of the base angles of the
triangle.
If the degree measure of each angle of a
triangle is 60, which of the following
statements is false?
a) The triangle is equiangular
b) The triangle is equilateral
c) The triangle is scalene.
d) The sum of the measure of the interior
angles of the triangle is 1800.
Find the degree measure of each of the acute
angles of an isosceles right triangle.
Aim: Isosceles Triangle
Course: Applied Geometry
Model Problem
Find the values of x and y.
B
What the diagram tells me:
BC  AB ABC is isosceles
x
A
CBD  ABD ( x)
y
90
angle bisector
63
mCDB = 90 = m y
D
C
In an isosceles triangle, the angle
bisector and altitude drawn from the
vertex angle, are the same line.
63 + 90 + CBD = 180
mCBD = 54 = mx
C  A = 63
Aim: Isosceles Triangle
Sum of angles of
a triangle equal
180.
Base angles of an isosceles
triangle are congruent
Course: Applied Geometry
Equilateral Triangle
An equilateral triangle has three equal sides.
R
P
O
If a triangle is equilateral, then it is equiangular
with each angle of the triangle measuring 60o.
All three special lines drawn from the each
angle of an equilateral triangle are the same
line.
Aim: Isosceles Triangle
Course: Applied Geometry
Model Problem
Find x.
x
65
x
Find x.
Aim: Isosceles Triangle
Course: Applied Geometry
Model Problem
Find x.
Find m & n.
W
50
Z
m
x
V
n
Y
VQ and YZ are
angle bisectors
Aim: Isosceles Triangle
Course: Applied Geometry
Model Problem
In triangle ABC, mA = x – 2, mB = 3x + 20
and mC = 5x. Find the value of x and the
measure of each angle
mA + mB + mC = 180.
x – 2 + 3x + 20 + 5x = 180
9x + 18 = 180
- 18 - 18
9x
= 162
mA = x - 2
9
9
18 - 2 = 16
x
= 18
mB = 3x + 20
3(18) + 20 = 74
mC = 5x
5(18)= 90
Aim: Isosceles Triangle
What type of
triangle is this?
Right Triangle
Course: Applied Geometry