1. Congruent Polygons 4.1

2. Objectives Define congruent polygons.
Solve problems by using congruent polygons.
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3. Glossary Terms corresponding angles corresponding sides
congruent polygons
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4. 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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5. 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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6. Angles and Line SegmentsX Y Z
50° A B C
50°
Angles are congruent when they have equal measures
(same number of degrees).
3 m
3 m
Line segments are congruent when they have equal lengths.
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7. 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 correspondence with the first polygon.
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8. 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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9. 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.
Sides:
Angles:
Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE  RTPSQ.
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10. Identify corresponding parts of congruent polygons.
Given: ABCD  WXYZ.
Identify all pairs of congruent sides and angles.
Congruent angles:
Congruent sides:
A  W
AB  WX
B  X
BC  XY
C  Y
CD  YZ
D  Z
DA  ZW
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11. 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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12. 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 pentagon MNOPQ.
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13. 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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14. Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DEF
Find the value of x.
2x – 2 = 6
2x = 8
x = 4
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15. Using Corresponding Parts of Congruent Triangles
In the diagram, ΔITP  ΔNGO. Find the values of x and y.
x – 2y = 7.5
x – 2(9) = 7.5
6y – 14 = 40
y = 9
6y = 54
x – 18 = 7.5
x = 25.5
Answer: x = 25.5, y = 9
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16. 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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17. Assignment
Geometry:
4.1A and 4.1B
Section