lesson 4-4 · 1 objective – to prove triangles congruent using sss and sas. sss congruence...
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1
Objective – To prove triangles congruent using SSS and SAS.
SSS Congruence PostulateIf 3 sides of a triangle are congruent to 3 sidesof another triangle, then the triangles are congruent.
SSS
If 3 sides are
3 angles will be
triangles will be
If 3 angles are
sides are notnecessarily
noconclusion
AAA
Reasons
Given: AD DCB is midpoint of AC Prove: ABD CBD
Statement
1) B is midpoint AC Given
A B
D
C
2) AB BC
3) BD BD
4) AD DC Given
Def. of Midpoint
Reflexive Prop. of
SSS Postulate5) ABD CBD
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X
1) Construct
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X
1) Construct
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X
1) Construct
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SASB
Steps
A
X
C
1) Construct
Lesson 4-4
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
2
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X
1) Construct 2) Copy adjacent side length
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X Z
1) Construct 2) Copy adjacent side length
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X Z
3) Copy other adjacent side
1) Construct 2) Copy adjacent side length
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
Steps
AC
X Z
3) Copy other adjacent side
1) Construct 2) Copy adjacent side length
B
SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Construction – Copy a Triangle Using SAS
StepsABC XYZ by SAS
AC
X Z
Y
3) Copy other adjacent side
1) Construct 2) Copy adjacent side length
Given: PM LN, LP PN, L NProve: LMP NMP
Statement
1) PM LN Given2) PML & PMN are rt. s 3) PML PMN All rt s are
L M
P
N
Reasons
Def. of lines3) PML PMN 4) L N
7) PM PM
5) LPM NPM
Given
6) LP PN
All rt. s are
Given
Reflexive Prop of 8) LMP NMP
Third Angles Thm.
SAS Postulate
Lesson 4-4
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
3
How can the triangles be proved congruent?
1)
SSS
3)
SAS
2)
SAS
4)
No Conclusion
How can the triangles be proved congruent?
5)
SAS
7)
SAS
6)
No Conclusion
8)
No Conclusion
Show that HIJ LMN if x 5.
H J
I N
3x 4
10 14
2x
L
M
19
4x 6
ML 2x 2(5) 10 HI ML HI ( )
MN 4x 6 4(5) 6 14 IJ MN IJ
HJ 3x 4 3(5) 4 19 LN HJ LN
HIJ LMN by SSS
Show that ABC JKL if n 4.
B C
A K
3n
58 142n 2
L
J
126n 8
2JL 2 2(4) 2 14 AC AC JL
32
2JL n 2 2(4) 2 14 AC AC JL
BC 3n 3(4) 12 KL BC KL
L 6n 8 6(4) 8 32 C C L
ABC JKL by SAS
Lesson 4-4
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014