Transcript Slide 1

Geometry Unit 4
When we talk about congruent triangles,
we mean everything about them Is congruent.
All 3 pairs of corresponding angles are equal….
And all 3 pairs of corresponding sides are equal
For us to prove that 2 people are
identical twins, we don’t need to show
that all “2000” body parts are equal. We
can take a short cut and show 3 or 4
things are equal such as their face, age
and height. If these are the same I think
we can agree they are twins. The same
is true for triangles. We don’t need to
prove all 6 corresponding parts are
congruent. We have 5 short cuts or
methods.
SSS
If we can show all 3 pairs of corr.
sides are congruent, the triangles
have to be congruent.
SAS
Show 2 pairs of sides and the
included angles are congruent and
the triangles have to be congruent.
Included
angle
Non-included
angles
ASA, AAS and HL
A
ASA – 2 angles
and the included side
AAS – 2 angles and
The non-included side
S
A
A
A
S
HL ( hypotenuse leg ) is used
only with right triangles, BUT,
not all right triangles.
HL
ASA
This is called a common side.
It is a side for both triangles.
We’ll use the reflexive property.
Which method can be used to
prove the triangles are congruent
Common side
SSS
Vertical angles
Parallel lines
alt int angles
Common side
SAS
SAS
When Starting A Proof, Make The
Marks On The Diagram Indicating
The Congruent Parts. Use The Given
Info, Properties, Definitions, Etc.
We’ll Call Any Given Info That Does
Not Specifically State Congruency
Or Equality A PREREQUISITE
SOME REASONS WE’LL BE USING
•
•
•
•
•
•
DEF OF MIDPOINT
DEF OF A BISECTOR
VERT ANGLES ARE CONGRUENT
DEF OF PERPENDICULAR BISECTOR
REFLEXIVE PROPERTY (COMMON SIDE)
PARALLEL LINES ….. ALT INT ANGLES
A
C
B
1 2
E
SAS
Given: AB = BD
EB = BC
Prove: ∆ABE =
˜ ∆DBC
Our Outline
P rerequisites
D S ides
A ngles
S ides
Triangles =˜
A
B
1
E
C
2
SAS
D
STATEMENTS
P
S
A
S
∆’s
Given: AB = BD
EB = BC
Prove: ∆ABE =
˜ ∆DBC
none
AB = BD
1=2
EB = BC
∆ABE =
˜ ∆DBC
REASONS
Given
Vertical angles
Given
SAS
C
12
Given: CX bisects ACB
A ˜= B
Prove: ∆ACX =˜ ∆BCX
AAS
A
X
B
P CX bisects ACB
A
1= 2
A
A= B
S
CX = CX
∆’s ∆ACX =˜ ∆BCX
Given
Def of angle bisc
Given
Reflexive Prop
AAS
Can you prove these triangles
are congruent?