Download Notes 4.1 Angles of a Triangle

September 19, 2011
Notes 4.1
Angles of a Triangle
Goals:
· Classify triangles according to sides and to angles.
· Apply the theorem and corollaries about the sum of the
measures of the angles of a triangle.
· Apply the theorem about the measure of an exterior
angle of a triangle.
Triangle -
In small groups, write the definition of the following words:
·
·
·
·
·
·
·
Scalene
Isosceles
Equilateral
Acute
Obtuse
Right
Equiangular
September 19, 2011
Scalene
· No sides are congruent
Isosceles
· At least two sides are
congruent
Equilateral
· All sides are congruent
Acute
· Three acute angles
Obtuse
· One obtuse angle
Right
· One right angle
Equiangular
· All angles are congruent
September 19, 2011
Triangle Sum Theorem
· The sum of the measures of the angles of a
triangle is _______.
Why?
Corollary
· A statement that can easily be proven by applying
a theorem.
Two Angles 3rd Angle Corollary
· If two angles of one triangle are congruent to two
angles of a second triangle, then the third angles
are congruent.
Equiangular Triangle Corollary
· Each angle of an equiangular triangle has a
measure of 60 degrees.
September 19, 2011
Corollary 3
· In a triangle, there can be at most one right angle
or obtuse angle.
Corollary 4
· The acute angles of a right triangle are
complementary.
Remote Interior Angles Theorem
· The measure of an exterior angle of a
triangle equals the sum of the measure
of the two remote interior angles
September 19, 2011
In
and an exterior angle at C is
five times as large as
Draw a picture and
solve.