Transcript Chapter 7

Chapter 7
Triangle
Inequalities
Segments, Angles and
Inequalities
Comparison Property
•For any two real numbers,
a and b, exactly one of the
following statements is
true.
a<b
a=b
ab
Theorem 7-1
• If point C is between points A
and B, and A, C, and B are
collinear, then AB AC and
ABCB.
Theorem 7-2
• If EP is between ED and EF,
then mDEF mDEP and
mDEF mPEF.
Transitive Property
•If a<b and b<c, then a<c.
•If ab and bc, then ac.
Addition and Subtraction
Properties
•If a<b, then a + c<b + c
and a - c<b – c
•If ab, then a + cb + c and
a - cb – c
Multiplication and Division
Properties
• If c0 and a<b, then ac<bc
and a/c<b/c
• If c 0 and a b, then ac bc
and a/c b/c
Exterior Angle Theorem
Exterior Angle
•An angle that forms a
linear pair with one of
the angles of a triangle
Remote Interior Angles
•The two angles in a
triangle that do not
form a linear pair with
the exterior angle
Exterior Angle Theorem
•The measure of an
exterior angle of a
triangle is equal to the
sum of the measures of
its two remote interior
angles.
Exterior Angle Inequality
Theorem
•The measure of an
exterior angle of a
triangle is greater than
the measure of either of
its two remote interior
angles.
Theorem 7-5
•If a triangle has one
right angle, then the
other two angles must
be acute.
Inequalities Within a Triangle
Theorem 7-6
•If the measures of three
sides of a triangle are
unequal, then the
measures of the angles
opposite those sides are
unequal in the same order.
Theorem 7-7
•If the measures of three
angles of a triangle are
unequal, then the
measures of the sides
opposite those angles are
unequal in the same order.
Theorem 7-8
•In a right triangle, the
hypotenuse is the side
with the greatest
measure.
Triangle Inequality Theorem
Triangle Inequality Theorem
•The sum of the measures
of any two sides of a
triangle is greater than the
measure of the third side.