Download Geometry Section 5.2 Congruent Polygons

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Transcript
Geometry Section 5.2
Congruent Polygons
What you will learn:
1. Identify and use corresponding parts
2. Use the third angle theorem
In simple terms, two polygons are congruent
if they have exactly the same size and shape.
More formally, two polygons are congruent iff a
rigid motion or composition of rigid motions maps
one onto the other.
* A rigid motion maps each part of the preimage
to a corresponding part in the image.
*Because rigid motions preserve angle measure
and side lengths,
corrsponding angles and sides are congruent
GE
EN
NO
GO
G
E
O
N
YS
ST
AT
AY
Y
S
A
T
congruence statement
YATS
DO
N
ACT
x28
x6
6  2 y  84
2 y  78
y  39
Theorem 5.4 Third Angles Theorem
If two angles of one triangle are congruent to
two angles of second triangle then, the third
angles are also congruent.
To prove two triangles are congruent using
the definition of congruent polygons, one
must show that all 6 pairs of corresponding
parts are congruent.
AO  ON
VOA & VON are Rt Ang.
VOA  VON
AVO  NVO
AVO  NVO
AVO  NVO
Given
Definition of midpoint
Definition of perpendicular
Right Angles Cong. Theorem
Definition of angle bisector
All Corr. Parts Cong.
AO  ON
VOA & VON are Rt Ang.
VOA  VON
AVO  NVO
AVO  NVO
VO  VO
AVO  NVO
Given
Definition of midpoint
Definition of perpendicular
Right Angles Cong. Theorem
Definition of angle bisector
Third Angle Theorem
Reflexive Property
All Corr. Parts Cong.
In subsequent sections, you will see that it is
possible to prove that some triangles are
congruent by using only three pairs of
congruent parts!
Theorem 5.3
Properties of Triangle Congruence
HW: p243 / 4-10, 12-14