Transcript Angles of a Triangle - Crestwood Local Schools

Classifying Triangles &
Angles of Triangles
Sections 4-1 & 4-2
A
triangle is the figure formed by 3
segments joining 3 noncollinear
points. Each of the 3 points is a
vertex. The segments are the sides.
Sides : AB, BC , CA
Vertices : points A, B, C
A
C
B
Classifying Triangles by Sides
Scalene Triangle –
no sides congruent
Isosceles Triangle –
At least 2 sides congruen
Equilateral Triangle –
All sides congruent
Classifying Triangles by Angles
700
500
Acute – 3 acute angles
600
Right – 1 right angle
400
1200
200
Obtuse – one obtuse angle
600
600
600
Equiangular – all angles congruent
Parts of an Isosceles Triangle
vertex angle
leg
base
base angles
leg
Angle Sum Theorem
The
sum of the measures of the
angles of a triangle is 180.
1000
400
400
Third Angle Theorem
 If
2 angles of one triangle are congruent to 2
angles of another triangle, then the third
angles are congruent.
Corollaries
statements that can be easily proved using a theorem
 Each
angle of an equiangular triangle has
measure 60.
 In a triangle, there can be at most one right
angle or obtuse angle.
 The acute angles of a right triangle are
complementary.
Exterior Angle Theorem
The
measure of an exterior angle of a
triangle equals the sum of the measures
of the 2 remote interior angles.
Remote interior
angles
350
Exterior
750
400
Joke Time
What
has wings and solves number
problems?
A
mothematician
What
did one math book say to the
other math book?
Don’t
bother me! I’ve got my own
problems!
What
would a math student say to a
fat parrot?
Poly-no-mial