Transcript Chapter 5 powerpoint


•
-Either a > b, a = b, or a < b
The Transitive Property
-If a > b, and b > c, then a > c
The Addition property
-If a > b, then a + c > b + c

The Subtraction Property
-If a > b, then a – c > b - c

The Multiplication Property
-If a > b, and c > 0, then ac>bc
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The Division Property-
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The Addition Theorem of Inequality
=>
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The “Three Possibilities” Property
-If a>b, and c>0, then a / c > b / c
-If a > b and c > d, then a + c > b + d
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The “Whole Greater than Part” Theorem
-If a > 0, b > 0, and a + b = c, then c > a and c > b
An exterior angle of a triangle is an angle
that forms a linear pair with an angle of
the triangle.
 Theorem- An Exterior angle of a triangle
is greater than either remote interior
angle.

<ACD is an
exterior angle of
ABC.
A
B
C
D
• <ACD > <A and <ACD > <B

Theorem- If two sides of a triangle are
unequal , the angles opposite them are
unequal in the same order.
A
C
line segment AB > line segment AC so <C > <B
B

(Converse) Theorem- If two angles of a
triangle are unequal, the sides opposite
them are unequal in the same order.
A
C
<C > <B, so line segment AB > line
segment AC
B

Theorem- The sum of any two sides of a
triangle is greater than the third side
A
C
AB + BC > AC
B
BC + AC > AB
AB + AC > BC

The Hinge Theorem-If two sides of one
triangle are equal to two sides of a
second triangle and if the included
angle of the first triangle is larger than
the included angle in the second
triangle, then the third side of the first
triangle is longer than the third side in
the second triangle. (Also known as the
SAS inequality Theorem)

The Converse to the Hinge Theorem-If
two sides of one triangle are equal to
two sides of a second triangle and if the
third side of the first triangle is larger than
the third side of the second triangle, then
the angle between the pair of
congruent sides of the first triangle is
larger than the corresponding included
angle in the second triangle.
In the lab we proved the exterior angle
inequality theorem- an exterior angle is
greater than either remote interior angles.
 We discovered that the sum of the two
shorter sides of a triangle must be greater
than the larger side – The Triangle inequality
theorem.
 We also constructed triangles to discover
that if two sides of a triangle are unequal
then their opposite angles are unequal in
the same order – Triangle Side and Angle
Inequalities ( Theorem + Converse)
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
Theorems
 Exterior Angle Theorem
 Triangle Side and Angle Inequality Theorem
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and Converse
 The Triangle Inequality Theorem
 The Hinge Theorem and Converse
Concepts
 Exterior angles
 The Properties of the Inequalities