Lesson 4-4 · 1 Objective – To prove triangles congruent using SSS and SAS. SSS Congruence Postulate If 3 sides of a triangle are congruent to 3 sides of another triangle, then
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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.
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