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Congruent Triangles
Congruent Polygons 4.1
Holt Geometry
Congruent Triangles
Objectives
• Define congruent polygons.
• Solve problems by using congruent polygons.
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Holt Geometry
Congruent Triangles
Glossary Terms
corresponding angles
corresponding sides
congruent polygons
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Holt Geometry
Congruent Triangles
Theorems, Postulates, &
Definitions
Polygon Congruence Postulate:
Two polygons are congruent if and only if there
is a correspondence between their sides and
angles such that:
1. Each pair of corresponding angles is congruent.
2. Each pair of corresponding sides is congruent.
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Holt Geometry
Congruent Triangles
Geometric figures are congruent if they are
the same size and shape.
Two polygons are congruent polygons if
and only if their corresponding sides and
angles are congruent. Thus polygons that are
the same size and shape are congruent.
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Holt Geometry
Congruent Triangles
Angles and Line Segments
X
A
50°
B
50°
C
Y
Z
Angles are congruent when they have equal measures
(same number of degrees).
Line segments are congruent when they have equal lengths.
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Holt Geometry
Congruent
Triangles
A correspondence is a way of matching up two
sets of objects.
To write a congruence statement, the vertices in
the second polygon have to be written in order of
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correspondence with the first polygon.
Holt Geometry
Congruent Triangles
How many ways can you name pentagon DCBAE?
Pick a vertex and go clockwise
Pick a vertex and go counterclockwise
AEDCB
ABCDE
BAEDC
BCDEA
CBAED
CDEAB
DCBAE
DEABC
EDCBA
EABCD
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Holt Geometry
Congruent Triangles
Identify corresponding parts of congruent polygons.
Show that the polygons are
congruent by identifying all of
the congruent corresponding
parts. Then write a
congruence statement.
Angles:
Sides:
Answer: All corresponding parts of the two polygons
are congruent. Therefore, ABCDE  RTPSQ. homework
Holt Geometry
Congruent Triangles
Identify corresponding parts of congruent polygons.
Given: ABCD  WXYZ.
Identify all pairs of
congruent sides and
angles.
Congruent angles:
A  W
B  X
C  Y
D  Z
Congruent sides:
AB  WX
BC  XY
CD  YZ
DA  ZW
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Holt Geometry
Congruent Triangles
Marking congruent sides and angles.
In the diagram below, mark the congruent parts of the two figures.
Then write a congruence statement.
Congruent Angles
A
M
B
N
C
O
D
P
Congruent Sides
AB MN
BC NO
CD OP
DA PM
Since A corresponds to M, B corresponds to N, C corresponds to
O,and D corresponds to P, a congruence statement is ABCD MNOP.
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Holt Geometry
Congruent Triangles
Write a congruence statement for each pair of
polygons.
The vertices in the first pentagon are written in order
around the pentagon starting at any vertex.
The congruence statement is pentagon
DEFGH  pentagon MNOPQ.
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Holt Geometry
Congruent Triangles
Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find the value of x.
2x – 16 = 90
2x = 106
x = 53
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Holt Geometry
Congruent Triangles
Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DEF
Find the value of x.
2x – 2
= 6
2x = 8
x=4
Holt Geometry
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Congruent Triangles
Using Corresponding Parts of Congruent Triangles
In the diagram, ΔITP  ΔNGO. Find the values of x and y.
6y – 14 = 40
6y = 54
y=9
Answer: x = 25.5, y = 9
x – 2y = 7.5
x – 2(9) = 7.5
x – 18 = 7.5
x = 25.5
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Holt Geometry
Congruent Triangles
In the diagram, ΔFHJ  ΔHFG. Find the values of
x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
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Holt Geometry
Congruent Triangles
Assignment
Geometry:
4.1A and 4.1B
Section 10 - 30
Holt Geometry