Download Triangles Part 1 The sum of the angles in a triangle is always equal to

Triangles Part 1
The sum of the angles in a
triangle is always equal to:
180°
Classification By Angle
Acute
A triangle that has all 3 acute angles
Obtuse
A triangle with one obtuse angle and 2 acute
angles
Right
A triangle with 1 right angle and 2 acute angles
The two acute angles must = 90° therefore they are
complimentary
Equiangular
A triangle with all 3 angles congruent
They must each = 60 °
Classification by Sides
Scalene
All three sides have different lengths
Isosceles
Two sides have the same length
Equilateral
All three sides have the same length
Isosceles Triangles
B
A
C
Equilateral Triangle
An equilateral triangle is also equiangular.
An equiangular triangle is also equilateral
B
A
C
Classify each triangle by its angles and sides.
Using the Distance Formula to classify
triangles by their sides
Find the measure of the sides of triangle DCE,
then classify the triangle by sides.
D(3, 9); E(5, 3);C(2, 2)
Step 1: Find the distance of all three sides using the distacne
formula. D =
(x2- x 1)2 + ( y2- y1)2
DE =
(-5 - 3) 2 + (3-9) 2 =
(-8) 2+(-6) 2 =
64+36 =
100 = 10
EC =
DC =
Step 2: Classify the traingle
Since _____ sides are congruent the traingle is called ______
You Try
Find the measure of the sides of RST. Classify
the triangle by sides.
R(1.  3);S(4, 4);T (8,1)
RS  74;ST  41; RT  85
 RST is Scalene
Find the missing Values
Find x and the measure of each side of
an equilateral triangle RST if:
RS  x  9;ST  2x; RT  3x  9
Step 1: Draw and equilateral traingle
and label the given information.
Step 1:
1: Draw
Draw and
and equilateral
equilateral
Step
SSS
traingle
and
label
the
givento
Step
2: Setand
anylabel
2 sides
traingle
the equal
given
information.
eachother
and solve for x. (It does
information.
not
matter
which two sides you
x+9
2x
x+9
2x
x+9
2x
choose
since
are equal)
Step 2:
Set all
anythree
2 sides
equal to eachother and
x=9
Step
3: Plug
into
onenot
side to get
solve
for x.x(It
does
TT
RR
T
R
allmatter
three side
lengths.
(To
check
which two sides you
your
answer
plug
x into are
the other
3x-9
choose
since
all three
3x-9
3x-9
two
sides
and
make
sure
all three
equal)
sides are equal.)
x+9 = 3x - 9
3x-9 = 2x
x+9 = 2x
RT
9 ==2x
-9 ==-x3x-9
RS
x +- 9
ST 9= =2xx
RT
18 = 2x
9 ==x3(9)-9
RS
9+9
ST = 2(9)
RT
= 27-9
9 ==x18
RS
ST = 18
RT = 18
You Try
Find d and the measure of each side of
an equilateral triangle KLM if:
KL  d  2; LM  12  d; KM  4d  13
d  5; KL  LM  KM  7
One more!
(This one is a little different)
Find x and the measure of all sides if COW is
isosceles, with CO=CW, and
CO  x  7;CW  3x  5;OW  x  1
x  6;CO  13,CW  13,OW  5
Finding the Measure of
Missing Angles
The sum of the angles in a
triangle is always equal to:
180°
Examples
Find X:
40°
2.)
x
1.)
65°
39°
x
4.)
3.)
2x
30°
x
x
Exterior Angle Theorem
The measure of an exterior angle of a
triangle is equal to the sum of the
remote interior angles.
Exterior Angle: An angle formed when one side of a triangle
is extended
Remote Interior Angles: The interior angles of the triangle
that are not adjacent to the exterior angle
4 is an exterior
angle
2
3
4
1
m1 + m 2 = m 4
1 & 2 are
remote interior
angles to 4
Proof of Exterior Angle Theorem
2
1
1.) m1 + m 2 + m 3 = 180
2.) m3 + m 4 = 180
3
4
By Def of a Triangle
By Def of Liner Pair
3.) m1 + m 2 + m 3 = m 3 + m 4 By Substitution
4.) m1 + m 2 = m 4
By SPOE
Bigger Picture
Find all missing angles
38°
4
5
32°
3
1
2
41°
64°