Post on 13-Dec-2015
4.9 Prove Triangles Congruent by SAS
Side-Angle-Side (SAS) Congruence PostulateIf 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 congruent.
_____,RS Side If UVand _____,R Angle U
_____,RT Side UW______ RSTthen UVW
S
R T
V
U W
4.9 Prove Triangles Congruent by SAS
Example 1 Use the SAS Congruence PostulateUse the SAS Congruence Postulate
RST.LMN that Show
M
N
L
R
S
T
SolutionIt is given that ,STMN ,RSLM and __________.
So, by the ____________________________,
._______LMN
SM SAS Congruence Postulate
RST
4.9 Prove Triangles Congruent by SAS
Hypotenuse-Leg Congruence TheoremIf 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 C
E
D F
4.9 Prove Triangles Congruent by SAS
Example 2 Use the HL Congruence TheoremUse the HL Congruence TheoremWrite a proof.Given: ,ECAC
,BDAB ,BDED
.BD ofbisector a is ACProve: EDCABC B
A
C
D
E
Statements Reasons
ECAC .1 _______ .1,BDAB .2 _______ .2
BDED
GivenGiven
4.9 Prove Triangles Congruent by SAS
Example 2 Use the HL Congruence TheoremUse the HL Congruence TheoremWrite a proof.Given: ,ECAC
,BDAB ,BDED
.BD ofbisector a is ACProve: EDCABC B
A
C
D
E
Statements Reasons
are D and B .3 lines of sDefinition .3 right angles ._____________
EDC and ABC .4 .___________are
_____ a of sDefinition .4__________right triangles
right
triangle
4.9 Prove Triangles Congruent by SAS
Example 2 Use the HL Congruence TheoremUse the HL Congruence TheoremWrite a proof.Given: ,ECAC
,BDAB ,BDED
.BD ofbisector a is ACProve: EDCABC B
A
C
D
E
Statements Reasons
bisector a is AC .5 ________ .5 Given.BD ofDCBC .6
EDCABC 7. bisectorsegment of sDefinition .6
_______________________ 7. HL Congruence Theorem
4.9 Prove Triangles Congruent by SASCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. Decide whether enough information is given to
prove ABC LMN using the SAS Congruence Postulate.
A
B C
N M
L,LMAB MNBC MB
Sides:
Included angle:
Therefore there is enough information
4.9 Prove Triangles Congruent by SASCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. Write a proof. P
S
Q
R
Given: ,QSPR ,SRPS SRQR
Prove: QSRPRS
Statements Reasons
QSPR .1 _______ .1SRQR ,SRPS .2 _______ .2
GivenGiven
are R and S .3 _____________________ .3 Definition of perp. lines.anglesright QSR and PRS .4
.nglesright tria are______________________ .4 Definition of a right triangle
4.9 Prove Triangles Congruent by SASCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. Write a proof. P
S
Q
R
Given: ,QSPR ,SRPS SRQR
Prove: QSRPRS
Statements Reasons
RSSR .5 _______________________ .5
QSRPRS .6 _____________________ .6Reflexive Property of Cong.
HL Congruence Theorem
4.9 Prove Triangles Congruent by SAS
Pg. 262, 4.9 #1-16