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Proving Congruence SSS, SAS
Chapter 4 Section 4
Learning Goal: Proving congruent triangles by SAS and SSS
Life is more accurately measured in the lives that you touch than
in the things you acquire
Why do we study Triangles
Architecture
Art
Sports
truss bridge
house trusses
tesselations
video
analysis
Congruence of Triangles--SSS
Notice the Corresponding Parts
∆ABC ∆ZXY ~=~=
Using SSS in proofs
E I
F H
First Draw your picture. . .
G ???
E
I F
H G
Prove: ΔFEG ΔHIG
Using SSS in proofs
E
I F
H G Prove: ΔFEG ΔHIG
Using SSS in proofs
1. Given
Statements
Prove: ΔFEG ΔHIG
3. SSS 3. ΔFEG ΔHIG
2. Def. of Midpoint 2.
1.
EI FH ~=~=
E
I F
H G
Proving Triangle Congruence
Reasons Proof:
Statements
3. SSS 3. ΔABG ΔCBG
1. Given 1.
2. _________ 2.
Congruence of Triangles -- SAS
Notice the parts correspond ∆ABC ∆FDE ~=~=
The angle is in the middle
and . . .
Congruence of Triangles -- SAS
Does the angle have to be in the middle?
4
3 5 3 4
A S S Watch out if it’s
not in the
middle Hyperlink to Geometry Chapter 4 ppt slide 148
C:\Program Files\07 GEOM TX IC\07GEOM Chapter 04.ppt
Coordinate Geometry
Use the Distance Formula to show that the corresponding sides are congruent.
Determine whether ΔWDV ΔMLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain
There is a Shortcut
Use Rise over Run and right triangles to
prove the distance is equal !!! It’s actually
SAS
Triangle Congruence
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
SSS
Triangle Congruence
Which postulate, if any, can be used to prove that the triangles are congruent?
SAS
Triangle Congruence
Which postulate, if any, can be used to prove that the triangles are congruent?
Not possible
Congruence in Right Triangles
15 15
7 7
HL – Hypotenuse Leg Triangles ~=~=Given:
A B
C
X Y
Z
Homework
Pages 230-232; #10, 15-18 all, 28, 31, 33, 35, 36-40(even), Copy the ∆ and do 44-49
(18 problems)
