Download Triangles and Angles

4.1 Triangles and Angles
Objective:
Classify triangles by their angles
and sides.
Triangles
• Triangle-figure formed
by 3 segments joining 3
noncollinear pts.
• Triangles are named by
these three pts (ΔQRS)
R
Q
S
Classifying Δs by Angles or Sides
Angles
• Acute
• Obtuse
• Right
• Equiangular
Sides
• Scalene
• Isosceles
• Equilateral
• Each of the three
pts are vertices
• Adjacent sides- 2
sides sharing a
common vertex
• Third side is
opposite the
given vertex.
B
A
C
Parts of a Right Triangle
Leg
Leg
Parts of an Isosceles Triangle
Leg
__
___
Base
Leg
How can ΔABC be right and
isosceles?
A
B
____
_____
C
Interior Angles
A
)))
B
C
Exterior Angles
(formed by extending the sides)
(
E
D
F
Thm 4.1:Triangle Sum Thm
• The sum of the measures
of the interior angles of a
triangle is 180o.
A
• mA + mB+ mC=180o
B
C
Thm 4.2: Exterior Angles Thm
• The measure of an
exterior angle of a
triangle is equal to the
sum of the measures
of the 2 nonadjacent
interior angles.
• m1=mA+ mB
B
A
1
C
Corollary to triangle sum thm
(Corollary- a statement
easily proved using a
thm.)
* The acute angles of a
right triangle are
complementary.
A
A is comp. to C
B
C
Assignment
Triangle worksheet