aim: isosceles triangle course: applied geometry aim: what is an isosceles triangle? do now: what...
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Aim: Isosceles Triangle Course: Applied Geometry
Aim: What is an Isosceles Triangle?
Do Now:
What type of triangle has sides of 3, 6, 8?
Aim: Isosceles Triangle Course: Applied Geometry
TrianglesA 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 2 equal No equal sides sides sides
Aim: Isosceles Triangle Course: Applied Geometry
Isosceles Triangle
A triangle with two sides that are equal in length.
AB BC
A C
Bleg
Base anglesBase
Base angles of an isosceles triangle are congruent
Isosceles Triangle
leg
Aim: Isosceles Triangle Course: Applied Geometry
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: mABQ = mCBQ Angle bisector of a triangle - A line segment that divides an angle of a triangle into two halves.
Aim: Isosceles Triangle Course: Applied 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
E G
F
H
Altitude - line segment from a vertex and perpendicular to the opposite side.
Median - A line segment from a vertex to the midpoint of the opposite side.
Angle bisector - A line segment that divides an angle of a triangle into two halves.
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
Complete each statement. Explain.
Model Problem
K
J
I
M
L
Na. _____ b. ____
. _____
KI KN
c ML
Aim: Isosceles Triangle Course: Applied Geometry
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
180o - 44o = 136o
2x = 136o
x = 68o
xo xo68o 68o
44o
Model Problem
Aim: Isosceles Triangle Course: Applied Geometry
Triangle ABC is isosceles with AB BC, AB = 3x - 2 and BC = 5x – 14. Find the value of x:
3x - 2 = 5x - 14-3x -3x - 2 = 2x - 14 +14 +14 +12 = 2x 6 = x
3(6) - 2= 163x - 2
5x - 145(6) - 14= 16
Model Problem
A
B
C
3x -
2 5x - 14
16 16
Aim: Isosceles Triangle 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 equiangularb) The triangle is equilateralc) 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.
y
x
63 D
B
C
AABC is isoscelesBC AB
CBD ABD
C A = 63
What the diagram tells me:
Base angles of an isosceles triangle are congruent
mCBD = 54 = mx
mCDB = 90 = m yIn an isosceles triangle, the angle bisector and altitude drawn from the vertex angle, are the same line.
angle bisector
63 + 90 + CBD = 180 Sum of angles of a triangle equal 180.
( x)90
Aim: Isosceles Triangle Course: Applied Geometry
Equilateral Triangle
P O
R
If a triangle is equilateral, then it is equiangular with each angle of the triangle measuring 60o.
An equilateral triangle has three equal sides.
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
x
Find x.
Find x.
65
x
Aim: Isosceles Triangle Course: Applied Geometry
Model Problem
Find x.
VQ and YZ are angle bisectors
x
Z
V Y
W
m n
50
Find m & n.
Aim: Isosceles Triangle Course: Applied Geometry
In triangle ABC, mA = x – 2, mB = 3x + 20 and mC = 5x. Find the value of x and the measure of each angle
x – 2 + 3x + 20 + 5x = 1809x + 18 = 180 - 18 - 189x = 1629 9 x = 18
mA = x - 2
mB = 3x + 20
mC = 5x
18 - 2 = 16
3(18) + 20 = 74
5(18)= 90
What type of triangle is this?
Right Triangle
Model Problem
mA + mB + mC = 180.