Proving Congruence SSS, SAS

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Transcript Proving Congruence SSS, SAS

Life is more accurately measured in the lives that you touch than
in the things you acquire
Proving Congruence SSS, SAS
Chapter 4 Section 4
Learning Goal: Proving congruent
triangles by SAS and SSS
Congruence of Triangles--SSS
Notice the
Corresponding Parts
∆ABC ~
= ∆ZXY
Using SSS in proofs
E
First Draw your
picture. . .
I
G ???
F
H
E
Prove: ΔFEG  ΔHIG
F
G
H
I
Using SSS in proofs
Prove: ΔFEG  ΔHIG
E
F
G
H
I
Using SSS in proofs
E
Prove: ΔFEG  ΔHIG
Statements
1.
EI ~
= FH
G
F
H
I
1. Given
2.
2. Def. of Midpoint
3. ΔFEG  ΔHIG
3. SSS
Proving Triangle Congruence
Proof:
Statements
Reasons
1.
2.
3. ΔABG ΔCBG
1. Given
2. _________
3. SSS
Congruence of Triangles -- SAS
Notice the parts
∆ABC
correspond
and . . .
The angle is in the middle
~
= ∆FDE
Congruence of Triangles -- SAS

Does the angle have to be in the middle?
5
3
3
4
4
SAS
Hyperlink to Geometry Chapter 4 ppt  slide 148
C:\Program Files\07 GEOM TX IC\07GEOM Chapter 04.ppt
Watch
out if it’s
not in
the
middle
Coordinate Geometry
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
the Distance
Formula
to show that the
Use
Rise over
Run
corresponding
sides
areand
right triangles to
congruent.
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
Z
C
7
A
7
15
15
B X
HL – Hypotenuse Leg
Given:
~
Triangles
=
Y
Homework

Pages 230-232; #10, 15-18 all, 28, 31, 33,
35, 36-40(even), Copy the ∆ and do 44-49
(18 problems)