1. Proving Triangles Congruent
Obj: SWBAT: 1) State the requirements for Congruency 2) Use the SSS and SAS Postulates to prove Triangle Congruency 3) Define, identify, and use the concept of an Included Angle
M11.C Identify and/or use properties of congruent and similar polygons or solids.

2. The Idea of a Congruence
Two geometric figures with exactly the same size and shape. A C B D E F

3. Congruent Polygons… Have congruent corresponding sides and angles
Specifically,  triangles have 3  corresponding sides and 3  corresponding <s

4. Corresponding Parts
If all 6 pairs of corresponding parts (sides and angles) are , then the triangles are . B A C
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F
ABC   DEF E D F

5. Steps and Tricks a) Reflexive Sides b) Vertical Angles
1. Mark everything that is given
2. BEWARE OF and MARK:
a) Reflexive Sides
(remember Reflexive Property of Congruence: AB  AB)
b) Vertical Angles
(across from each other and  )
3. Look for short-cuts that match the theorems

6. Do you need all 6 ?
NO !
SSS
SAS
ASA
AAS

7. Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF
SSS: If 3 sides of 1 triangle are  to 3 sides of another triangle, then the 2 triangles are .

8. Side-Angle-Side (SAS)B F A D C
AB  DE
A   D
AC  DF
ABC   DEF
included
angle
SAS: If 2 sides of 1 triangle are  to 2 sides of another triangle and the included < of 1 triangle is  to the included < of another triangle, then the 2 triangles are .

9. Included Angle
Is the < between or INside 2 sides
 H
 G
 I

10. Included Angle Name the included angle: YE and ES ES and YS YS and YE

11. Name That Postulate
(when possible)
SAS
SAS
ASS
SSS

12. Name That Postulate SAS SAS ASS SAS Vertical Angles Reflexive Property
(when possible)
Vertical Angles
Reflexive Property
SAS
SAS
Vertical Angles
Reflexive Property
ASS
SAS