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TRIANGLES
• Equilateral
• Isosceles
• Scalene
 Right
 Acute
 Obtuse
TRIANGLES
•
Equilateral: A triangle with 3 congruent sides.
Equilateral: A triangle with
3 congruent ANGLES.
•
Isosceles: A triangle with 2 congruent sides.
•
Scalene: A triangle with no congruent sides.
TRIANGLES
•
Acute: A triangle with 3 acute angles.
•
Right: A triangle with one right angle.
•
Obtuse: A triangle with one obtuse angle.
PARTS OF A TRIANGLE
Every triangle is made up of three sides connected by vertexes.
side
vertex
Triangle Sum Theorem: The sum of the measurements of each triangle add up to
180º.
60º
60º
50º
xº
X = 60º (60+60+60=180)
90º
xº
X=40º (90+50+40=180º)
EXTERIOR AND INTERIOR ANGLES (TRIANGLE
PARTS CONT.)
•
Exterior Angle: The angle formed outside the angle when an extension is drawn to
the triangle.
•
Interior Angle: Any angle formed inside the triangle.
EXTERIOR ANGLE THEOREM
•
We can use this theorem when we need to find an angle and an exterior angle is
available. We can use this theorem when a triangle shape is used in a
construction.
•
m<4 = m<1 + m<2
•
Examples:
55º
45º
x=85º
65º
50º
xº
yº
y=60º
35º
z=55º
90º
zº
CONGRUENCE IN SHAPES AND CTCP
•
A shape is congruent to the other if they have the same shape, size, and
measure.
•
CPCT: Corresponding Parts of Congruent Triangles.
•
EXAMPLES:
A
w
3 cm.
6 cm.
B
x
CD=3 cm.
D
t
s
yz=6 cm.
y
C
2.4 ft.
z
v
uv=2.4 ft.
u
SSS
Side-side-side: if the two triangles have three congruent sides, then the triangles
themselves are congruent.
6 cm.
6 cm.
6 cm.
6 cm.
6 cm.
8 cm.
8 cm.
5 cm.
6 cm.
8 cm.
8 cm.
5 cm.
These two triangles are
congruent to each
other.
SAS
Side-angle-side: If two sides and the angle in a triangle are congruent to the other two
sides and the angle in another triangle, the both triangles are congruent to each
other.
ASA
Angle-side-angle: if the two angles and the side on each triangle are congruent to
each other, then the triangles themselves are congruent.
AAS
Angle-angle-side: If the two angles and the side are congruent, then the triangles
themselves are congruent.