Download Chapter 10 Introducing Geometry

2/3/2010
Congruent Triangles
Chapter 10
Introducing Geometry
Congruent triangles: each pair of
corresponding sides are congruent
and each pair of corresponding
angles
l are congruent.
t
Section 10.4
More About Triangles
Triangle Congruence
Postulates and Theorems
Side-Side
SideSide--Side (SSS) Postulate
Side--Angle
Side
Angle--Side (SAS) Postulate
Angle--Side
Angle
Side--Angle (ASA) Postulate
Angle--Angle
Angle
Angle--Side (AAS) Theorem
Hypotenuse--Acute Angle (HA) Theorem
Hypotenuse
Hypotenuse--Leg (HL) Theorem
Hypotenuse
Similar Triangles
Similar Triangles: each pair of
corresponding angles are
congruent and the ratios of
corresponding
di sides
id are equal.
l
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Triangle Similarity
Postulates and Theorems
AA Similarity Postulate
Right Triangle Similarity Theorem
SAS Similarity Theorem
SSS Similarity Theorem
The Pythagorean Theorem
In a right triangle, the square of the
length of the hypotenuse equals the
sum of the squares of the lengths of
the legs
legs.
a² + b² = c²
leg² + leg² = hypotenuse²
Example
A farmer has a rectangular paddock,
125 yards by 100 yards, that he wishes
to divide into two smaller, equal
paddocks by installing a new fence
along the diagonal of the paddock.
Find the perimeter of one of the new
paddocks.
Special Right Triangles
45 - 45 - 90 Triangle
The length of the hypotenuse of any 45 - 45 90 triangle is the length of a leg times
.
2
30 - 60 - 90 Triangle
The length of the hypotenuse of any 30 - 60 90 triangle is 2 times the length of the shorter
leg. The length of the longer leg is the length
of the shorter leg times
3 .
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