Transcript Document 7389711

4.9
Prove Triangles Congruent by SAS
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle
are congruent to two sides and the included angle
of a second triangle, then the two triangles are
S
congruent.
If Side RS  _____,
UV
Angle R  
_____,
U and
R
Side RT  _____,
UW
then RST  ______
UVW
V
T
U
W
4.9
Prove Triangles Congruent by SAS
Example 1 Use the SAS Congruence Postulate
Show that LMN  RST.L
T
S
M
Solution
N R
M  S
It is given that LM  RS, MN  ST, and __________.
So, by the ____________________________,
SAS Congruence Postulate
ABC  _______
RST .
4.9
Prove Triangles Congruent by SAS
Hypotenuse-Leg Congruence Theorem
If the hypotenuse and a leg of
a right triangle are congruent
to the hypotenuse and a leg of
a second right triangle, then
the two triangles are
congruent
___________.
B
A
E
C D
F
4.9
Prove Triangles Congruent by SAS
Example 2 Use the HL Congruence Theorem
E
Write a proof.
Given: AC  EC ,
A
AB  BD,
ED  BD,
AC is a bisector of BD.
Prove: ABC  EDC
Statements
Reasons
1. AC  EC
2. AB  BD,
ED  BD
1.
2.
D
B
Given
_______
Given
_______
C
4.9
Prove Triangles Congruent by SAS
Example 2 Use the HL Congruence Theorem
Write a proof.
Given: AC  EC ,
E
A
AB  BD,
ED  BD,
AC is a bisector of BD.
Prove: ABC  EDC
Statements
D
B
C
Reasons
3. B and D are 3. Definition s of  lines
right angles___.
__________
right
4. ABC and EDC 4. Definition s of a _____
triangles_ .
triangle
__________
are right
__________
4.9
Prove Triangles Congruent by SAS
Example 2 Use the HL Congruence Theorem
Write a proof.
Given: AC  EC ,
E
A
AB  BD,
ED  BD,
AC is a bisector of BD.
Prove: ABC  EDC
D
B
Statements
Reasons
5. AC is a bisector
of BD.
6. BC  DC
7. ABC  EDC
Given
5. ________
C
6. Definition s of segment bisector
HL Congruence
Theorem___
7. __________
__________
4.9
Prove Triangles Congruent by SAS
Checkpoint. Complete the following exercises.
1. Decide whether enough information is given to
prove ABC  LMN using the SAS
B
C
Congruence Postulate.
AB  LM , BC  MN
Included angle: B  M
L
Sides:
Therefore there is
enough information
A
N
M
4.9
Prove Triangles Congruent by SAS
Checkpoint. Complete the following exercises.
2. Write a proof.
P
Q
S
R
Given: PR  QS, PS  SR , QR  SR
Prove: PRS  QSR
Statements
Reasons
1.
1. PR  QS
2. PS  SR , QR  SR 2.
3. S and R are 3.
right angles .
4. PRS and QSR 4.
are right tria ngles .
Given
_______
Given
_______
Definition of__________
perp. lines _
__________
Definition
of a__________
right triangle
__________
__
4.9
Prove Triangles Congruent by SAS
Checkpoint. Complete the following exercises.
2. Write a proof.
P
Q
S
R
Given: PR  QS, PS  SR , QR  SR
Prove: PRS  QSR
Statements
Reasons
5. SR  RS
6. PRS  QSR
Property
of Cong.
5. Reflexive
__________
__________
___
HL Congruence
Theorem_
6. __________
__________
4.9
Prove Triangles Congruent by SAS
Pg. 262, 4.9 #1-16