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Geometry Journal 4
Andres Cofiño
Types of Triangles
Equiangular: is a triangle that all angles in it have the same
measure
Equilateral: is a triangle that all sides of it have the same
measure
Scalene: is a triangle that have no equal sides nor angles
Isosceles: is a triangle that two of its sides are congruent to
each other
Right triangle: is a triangle that has one angle that its measure is
90 degrees
Obtuse triangle: is a triangle that has one angle that its measure
is greater then 90 degrees.
Triangles are classified either by its angles or sides,
although they can be classified by both (sides and angles).
Obtuse triangle
Right triangle
Equilateral triangle
Scalene Triangle
Isosceles triangle
Parts of Triangle
Triangles consist in three angles and three sides.
three angles
“tri” =
Triangle Sum Theorem says that the sum of the three angles
of a triangle equals 180 degrees.
Examples
60^
60+60+60=180
120^
60^
60^
34^
120+34+26=180
80^
40^
60^
80+60+40=180
26^
Exterior Angle Theorem
Says that any exterior angle of a triangle is always equal to the
sum of the two non-adjacent sides.
50^
40^
100^
40^
100^
80^
80^
50^
60^
60^
120^
Exterior Angle Theorem can be used to measure a table or any other
triangular/rectangular object.
CPCT
Congruence for shapes consist of having same exact
measures of angles and sides.
CPCT- Corresponding Parts of Congruent Triangles is when
you have proved two triangles are congruent so each part of
one triangle (either side or angle) is congruent to the same
side or angle of the other triangle.
B
A
5
5
7
5
C
B
7
C
5
A
5
6
4
6
4
5
S
W
S
W
Q
Q
SSS
Side Side Side postulate says that if three sides of a triangle are
congruent to three sides of another triangle, then these two
triangles are congruent.
5
E
5
5
5
5
J
Q
5
K
L
2
1
QE congr. JL
QW congr. JK
WE congr. KL
3
3
2
W
1
WQE congruent KJL
SAS
Side Angle Side postulate says that if two sides and included
angle of a triangle are congruent to two sides and the included
angle of another triangle, then those triangles are congruent.
3
5
90^
8
10
60^
4
4
45^
5
5
10
60^
45^
5
90^
3
8
ASA
The Angle Side Angle postulate says that if two angles and the
included side of a triangle are congruent to two angles and the
included side of another triangle, then both triangles are
congruent.
8
45^
90^
90^
30^
9
70^ 70^
90^
45^
8
4
70^
70^
4
9
30^
90^
AAS
The Angle Angle Side postulate says that if two angles and
the non-included side of a triangle are congruent to two
angles and the non-included angle of another triangle, then
these two triangles are congruent.
45^ 90^
11
60^
7
60^
60^
60^
7
11
90^
45^