4.4 ½: More Practice with Congruent Triangles
"Where
"Where Do
Do these
these stairs
stairs go?"
go?" -Ray
-Ray
"They
"They go
go up."
up." -- Peter
Peter
Proving Triangles Congruent
Can we use the given information to prove triangles congruent?
Proving Triangles Congruent
B
C
E
A
Given
Midpoint
Segment bisects
a segment
Look For…
D
Reason
Example
Two segments
are congruent
Defn. of midpoint
Two segments
are congruent
Defn. of bisector
If E is the midpoint of AC
then AE  CE
If AC bisects BD
then BE  DE

Two segments
parallel
Alt. int. angles
congruent
Alt. int. angles
theorem 
Vertical angles
Two congruent
angles
Vert. angles
theorem

If BA || CD
then A  C
and B  D
BEA  DEC
Proving Triangles Congruent
X
W
Given
Look For…
Segment bisects
an angle
Two angles
are congruent
Triangles that
share a side
A segment
congruent to itself
1 2
Z
Y
Reason
Example
Defn. of
angle bisector
Reflexive property

of congruence
If XZ bisects WXY
then WXZ  YXZ
XZ  XZ
If XZWY
Perpendicular
segments
Two angles
are congruent
1) Right angles by 
then 1, 2 are right 's
defn. of  lines
2) All right angles  then 1  2


Proving Triangles Congruent
B
C
Given : E is the midpoint of AC and BD
Prove : A  C
E
A
Statements
Reasons
D
Proving Triangles Congruent
Practice Time!!!!