1. Congruent Triangles

2. Helpful websites

3. 4-1 Congruent Figures
Objective: To recognize congruent figures and their corresponding parts

4. Vocabulary/ Key Concept
Congruent polygons-
two polygons are congruent if their corresponding sides and angles are congruent
If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.

5. Each pair of polygons are congruent
Each pair of polygons are congruent. Find the measure of each numbered angle
M1 = 110
m 2 = 120
M3 = 90
m 4 = 135

6. WXYZ  JKLM. List 4 pairs of congruent sides and angles.
WX  JK
XY  KL
YZ  LM
ZW MJ
W  J
K  X
Y  L
Z  M

7. Determine if the polygons are congruent. Explain.
1.G  I , GJH  IJH, 2.GHJ  IHJ 3. JI GJ, GH  IH, 4. JH  JH GHJ and IHJ are congruent because all corresponding angle and sides are congruent
1.Given –congruent markings
2.If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.
3.Given-congruent markings
4.Reflexive

8. Determine if the polygons are congruent. Explain.
1.Q  T 2.QSR  TSV 3.R  V No, the triangles do no have corresponding sides that are congruent
1.Given – congruent measures 2.Vertical angles 3. If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.

9. PROOF
Statement 1. LM  QP LN QN MN  PN  L  Q 2.  LNM  QNP 3. P  M 4. LMN  QPN
Reasons
GIVEN
VEERITCAL ANGLES
If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent
4. Def. of congruent polygons

10. 4-2 Congruent Triangles by SSS and SAS
Objective: To prove two triangles are congruent using SSS and SAS Postulates

11. Key Concepts SSS – Side-side-side corresponding congruence.
SAS – Side-Angle-Side corresponding Congruence.
ANGLE MUST BE IN BETWEEN THE TWO SIDE

12. Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.
AB  CB --CONGRUENCE MARKING
BD  BD -- REFLEXIVE
ABD  CBD –CONGRUENCE MARKING
 ABD   CBD by SAS

13. Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.
What do you know? NP = QP -- CONGRUENT MARKS NR = QR -- CONGRUENT MARKS RP = RP -- REFLEXIVE PROPERTY OF 
 PRN   PRQ by SSS

14. Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.
EM  PQ EN  PR CONGRUENCE MARKING N  R
Not possible

15. Proof Statements Reasons AB  DC, BAC  DCA Given
AC  CA
ABC  CDA
Reasons
Given
Reflexive property of 
SAS
A B
D C

16. Try: Write a proof. Statement EF GF, HF  DF  DFE  HFG
Reasons
Given
Vertical angles
SAS

17. 4-3 Congruent Triangles by AAS and ASA
Objective: To prove two triangles are congruent using AAS and ASA Postulates

18. Key Concepts ASA – Two angles and an included side.
AAS – Two angles and a non-included side.
SIDE IS IN BETWEEN THE ANGLES

19. Determine if you can use ASA or AAS to prove two triangles are congruent. Write the congruence statement.
TUV VST by ASA not possible BCEDCF by AAS

20. Write a Proof Statement KL ML,  K  M  JLK   PLM  JKL  PML
Reasons
Given
Vertical angles
ASA

21. What did you learn today?
What are some simple steps to writing proofs?
What are the four ways to prove triangles are congruent?