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OTCQ
RGT is adjacent to angle
TGL.
If m
◦
RGL = 100 and
What is m
RGT?
m
◦
TGL = 20 ,
OTCQ
RGT is adjacent to angle
TGL.
If m
◦
RGL = 100 and
What is m
RGT?
G
80 ◦
L
◦
TGL = 20 ,
m
R
20 ◦
T
Aims 1-6 & 1-7 How do we define angles
and triangles?
NY GG 31, GG 32, GG 33, GG 35, GG 28
Read 1-6 and 1-7 do problems 18 -25 on
page 22.
1-6 & 1-7 objectives
1.
2.
3.
4.
SWBAT name angles and angle parts.
SWBAT define:
congruent angles, complimentary angles,
supplementary angles and adjacent angles
Bisector of an angle
Perpendicular line
Distance from a point to a line
SWBAT add angles.
SWBAT define a triangle and its parts.
• An angle consists of two different rays that
have the same initial point.
• The rays are the sides of the angle.
• The initial point A is the vertex of the angle.
• The angle that has rays AB and AC as
sides may be named BAC, CAB, or A.
B
sides
Vertex
A
C
The set of all points between the
sides of the angle is the interior
of an angle.
The exterior of an angle is the
set of all points outside the angle.
Angle Name
R, SRT, TRS, or 1
If the point is the vertex of more than one angle,
you must use all three points to name the angle.
The middle point is always the vertex.
The measure of A is denoted by mA.
The measure of an angle can be
approximated using a protractor, using units
called degrees(°).
BAC has a measure of 50°, which can be
written as mBAC = 50°.
B
C
A
Angle Relationships
Congruent Angles: Angles with equal measures in
degrees.

MSU
RWE
EWR
or
M

USM
W
E
R
S
U
Angle Relationships
• Complementary Angles: Two angles
are called complementary angles if
the sum of their degree
measurements equals 90° degrees.
• Supplementary Angles: Two angles
are called supplementary angles if
the sum of their degree
measurements equals 180°
degrees.
Angle Relationships
• Adjacent Angles: Share a
vertex and a common side but
no interior points.
• Bisector of an angle: a ray
that divides the angle into two
congruent angles.
OY
is the angle bisector.
What are perpendicular
lines?
• Two lines that
◦
intersect at a 90
angle (right angle)
are Perpendicular
lines.
• Boxed vertex
◦
means 90
The shortest distance from a point to a line will
always be the distance of the perpendicular line
from the point to the line.
Boxed
vertex
means
90
◦
Adding Angles
 When you want to add angles, use the notation m1,
meaning the measure of 1.
 If you add m1 + m2, what is your result?
m1 + m2 = 58.
A
B
36°
m1 + m2 = mADC also.
22°
1
Therefore, mADC = 58.
D
2
C
Congruent

Angles that measure the same in degrees are
congruent.
PET
TEJ
J
LEP
E
L
T


JEL

P
Symbol for congruent
Congruent

Explain why the angles are congruent.
J
PET
LEP
E
L
T


TEJ
JEL

P
Symbol for congruent
Congruent

They are all 90◦
PET
J
LEP
E
L
T


TEJ
JEL

P
Symbol for congruent
Congruent


Segments that measure the same in inches, feet,
miles, milimeters, centimeters, meters, or
kilometers are called congruent.
A
T
P
C
___
AT

___
PC
Symbol for congruent
1-6 & 1-7 objectives CHECK UP
1.
2.
3.
SWBAT name angles and angle parts.
SWBAT define:
congruent angles, complimentary angles,
supplementary angles and adjacent angles
Bisector of an angle
Perpendicular line
Distance from a point to a line
SWBAT add angles.
4.
NEXT:SWBAT define a triangle and its parts.
Polygon: A closed plane
figure formed by three or more
line segments that meet only
at their endpoints.
Triangle: a polygon with exactly 3 sides.
Types of Triangles:
Equilateral
all 3 sides
and angles
are
congruent.
Also called
Equiangular.
Isosceles
Triangle— 2 or
3 sides/angles
are congruent
Scalene—
no sides or
angles are
congruent
Triangle Parts:
• 3 vertices: A, B, C.
• 3 line segments:
__
__
__
BC , CA & AB
• Any 2 line segments in
a triangle that share a
common endpoint are
called adjacent sides.
__
CB is the opposite
side of endpoint A
C
B
__
__
CA and BA share endpoint A, so they are adjacent sides.
__
__
CB and BA share endpoint B, so they are adjacent sides.
__
__
BC and CA share endpoint C, so they are adjacent sides.
A
EQUILATERAL is EQUIANGULAR
• 3 congruent 60◦ acute angles (“equiangular”).
• 3 congruent line segments. (“equilateral” ).
• Acute.
• Can’t be right
• Also isosceles
because at least 2 sides/angles are congruent.
• Each line segment is a side.
Isosceles Triangles need only 2
congruent sides/angles.
• The 2 congruent sides are
called legs. Green dashes
means congruent.
• The noncongruent side is
called the base. No green
dashes.
• The 2 congruent angles
are called base angles.
Blue arc means
congruent.
• The noncongruent angle is
called the vertex angle. No
blue arcs.
Vertex
Angle
leg
leg
Base
Base
Base
Angle
Angle
ISOCELES
Right Triangle
45◦
45◦
base • The red side is both a
hypotenuse
and
a
base.
angle
• The boxed 90◦ right
leg
angle is the vertex angle.
Hypotenuse
base
leg
◦
45
Base angle
• A right triangle with 2
congruent sides/angles, is
an isosceles right triangle.
• its base angles are each
90◦
vertex
• Green dashes mean
congruent.
• Blue arcs mean
congruent.
Acute Triangle: an acute triangle has 3 acute
angles.
Could be equilateral/equiangular (all
= 60◦).
Could be isosceles ∆ or scalene ∆ but never a
right
and never an obtuse ∆.
m ABC = 70.26 
m CAB = 41.76 
m BCA = 67.97 
B
C
A
Right Triangle
• 1 right angle
Obtuse Triangle: has
one obtuse angle.
Right and Obtuse triangles are never acute or
equilateral, but can be isosceles (have 2
congruent sides/angles).
Right Triangle
hypotenuse
leg
• Red represents the
hypotenuse of a right
triangle.
• The blue sides that
form the right angle
leg
are the legs.
What is this?
leg
base
leg
What is this? An
isosceles triangle.
leg
base
leg
Quick Algebra Review
Commutative Property
Commutative Property of Addition: a + b = b + a
Commutative Property of Multiplication: ab = ba
Examples
2+3=5=3+2
3• 4 = 12 = 4 • 3
The commutative property does not
work for subtraction or division!!!!!!!!
Associative Property
Associative property of Addition:
(a + b) + c = a + (b + c)
Associative Property of Multiplication:
(ab) c = a (bc)
Examples
(1 + 2) + 3 = 1 + (2 + 3)
(2 • 3) • 4 = 2 • (3 • 4)
The associative property does not work for subtraction
or division!!!!!
Identity Properties
1) Additive Identity
a+0=a
2) Multiplicative Identity
a•1=a
Inverse Properties
1) Additive Inverse (Opposite)
a + (-a) = 0
2) Multiplicative Inverse (Reciprocal)
1
a
 1
a
Multiplicative Property of Zero
a•0=0
(If you multiply by 0, the answer is 0.)
The Distributive Property
Any factor outside of expression enclosed within
grouping symbols, must be multiplied by each
term inside the grouping symbols.
Outside left
a(b + c) = ab + ac
a(b - c) = ab – ac
or
Outside right
(b + c)a = ba + ca
(b - c)a
= ba - ca
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