1. Congruence and triangles
Chapter 4 Section 4.2
Congruence and triangles

2. Warm-Up

3. Congruent Figures
Two geometric figures are congruent if the have exactly the same size and shape
When figures are congruent
Corresponding angles are congruent
Corresponding sides are congruent
Yes, all corresponding parts are 
Are these two  ?

4. Writing congruence statements
When writing a congruence statement it is important that the pieces correspond in the statement just like in the picture.

5. A M T C D N

6. T 48
5 cm 73
JTM

7. Third Angle Theorem
If two angles of a triangle are congruent to two angles of another triangle, then the third angles are also congruent
A  D and B  E thus C  F

8. Proving Figures Are Congruent
To prove two geometric figures congruent
Must show all corresponding angles are 
Must show all corresponding sides are 

9. Determine If the Figures Can Be Proven Congruent
Given
DEG  FGE
Given
D  F
Right Angle Thm
DGE  FEG
Third Angle Theorem
Reflexive
Yes DGE  FEG
Def.  ’s

10. Determine If the Figures Can Be Proven Congruent
Given
N  R
Given
P  T
M  Q
No ’s not 

11. Determine If the Figures Can Be Proven Congruent
Given
X  Z
Given
XYW  ZYW
Right Angle Thm
XWY  ZWY
Third Angle Theorem
Reflexive
Yes XYW  ZYW
Def.  ’s

12. Use the given information to find the values of x and y

13. Use the given information to find the values of a and b
mT = 6(9) – 3 = 51
mT + mR + mS = 180
mS = 180
mS = 180
mS = 46
6a – 3 = 51
6a = 54
a = 9
7b – 10 = 46
7b = 56
b = 8