1. Find the value of x
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5.2 Congruent Polygons

2. Geometry
5.2 Congruent Polygons

3. Essential Question
Given two congruent triangles, how can you use rigid motions to map one triangle to the other triangle?
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5.2 Congruent Polygons

4. Goals Identify Congruent Figures. Name Corresponding Parts.
Prove Triangles Congruent.
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5.2 Congruent Polygons

5. Congruent Figures
Two figures are congruent if they have exactly the same shape and same size.
These figures are congruent:
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5.2 Congruent Polygons

6. So are these:
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5.2 Congruent Polygons

7. These are not congruent:
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5.2 Congruent Polygons

8. If two figures are congruent, then there is a correspondence between them.
Corresponding Angles
A  R
B  S
C  T
Corresponding Sides R S T
AB  RS
BC  ST
AC  RT
ABC  RST
Congruence Statement
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5.2 Congruent Polygons

9. ABC  RST You could also write: BAC  SRT CAB  TRS ACB  RTS
BCA  STR
CBA  TSR A B C R S T
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5.2 Congruent Polygons

10. B is NOT congruent to T.
But you cannot write:
ABC  RTS A B C
B is NOT congruent to T. R S T
When writing a congruence statement, corresponding parts must be matched correctly.
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5.2 Congruent Polygons

11. Example 1 NSRM BADC  SNMR ABCD  CDAB  RMNS ADCB  NMRS
Write a congruence statement for these congruent figures. A M N B C S D R
NSRM
ABCD 
BADC 
SNMR
CDAB 
RMNS
ADCB 
NMRS
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5.2 Congruent Polygons

12. Example 2 In this diagram, RST  XYZ. R S  ______ Y X  ______
85° 12
40° R
S  ______ Y
X  ______
YZ = ______ 12
RS = ______ XY
mS = ______
85°
40°
mX = ______
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5.2 Congruent Polygons

13. Your Turn ABCD  KJHL. Solve for x and y. 4x – 3 = 9 5y – 2 = 113
You cannot trust pictures. Always use the given congruence statement. A
9 cm B L K
91°
4x – 3 cm
86°
113°
(5y – 2)° J D C H
6 cm
4x – 3 = 9
4x = 12
x = 3
5y – 2 = 113
5y = 115
y = 23
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5.2 Congruent Polygons

14. Theorem 5.3 Prop. of Triangle Congruence
Reflexive: Every Triangle is congruent to itself. ABC  ABC.
Symmetric: If BAD  DOG, then DOG  BAD.
Transitive: If ABC  DEF, and DEF  RST, then ABC  RST.
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5.2 Congruent Polygons

15. Theorem 5.4 Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. A B C D E F
If A  D and B  E, then C  F.
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5.2 Congruent Polygons

16. Example 3 ABC  DEF. Find x. A B C 22° 87° D E F (4x + 15)°
Using Triangle Angle Sum Theorem:
mA = 180
mA = 180
mA = 71
Using Third Angles Theorem
mA = 4x + 15
71 = 4x + 15
56 = 4x
x = 14
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5.2 Congruent Polygons

17. Proving Triangles Congruent
Two triangles are congruent if you can show that all three corresponding sides are congruent, and all three corresponding angles are congruent.
2 s   3 s & 3 sides .
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5.2 Congruent Polygons

18. Example 4 BAT  MAN Is BAT  MAN? M T 58 A 58 N B
Using the segment marks:
Angles:
B  M (same measure)
BAT  MAN (why?)
T  N (why?)
Three angles congruent.
AT  AN
BT  MN
AB  AM
(Vert s)
(3rd s theorem)
Three segments congruent.
BAT  MAN
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5.2 Congruent Polygons

19. What have you learned? Your Turn to Practice! 1. Given ABC  DEF.
a. Name three pairs of
congruent sides.
b. Name three pairs of
congruent angles. A C B D
AB & DE, BC & EF, AC & DF F E
M &  P, N & Q, O & R
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5.2 Congruent Polygons

20. Your Turn to Practice!
2. In the diagram, MKL  JET. Complete the following statements.
L  ___
𝑀𝐾  ___
mM = ___
mT = ___
ML = ___
ETJ  _____ M T 𝐽𝐸
32° K L
85° J
63°
85°
6 cm
6 cm E T
KLM
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5.2 Congruent Polygons

21. Your Turn to Practice! 3. Complete the statement.
a. If WRD  PLK, then 𝑊𝑅  _____.
b. If BGT  DSN, then ∠ 𝑇  _____.
c. If JCX  MWP, then 𝑋𝐶  _____.
d. If RHK  WVO, then KRH  _____. 𝑃𝐿
∠ 𝑁 𝑃𝑊
OWV
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5.2 Congruent Polygons

22. Summary If two figures are congruent, then…
corresponding angles are congruent,
corresponding sides are congruent.
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5.2 Congruent Polygons

23. Assignment
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5.2 Congruent Polygons