CONGRUENT

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CONGRUENT TRIANGLES
Sections 4-2, 4-3, 4-5
Jim Smith JCHS
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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
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For us to prove that 2 people are identical
twins, we dont 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 dont need to prove all 6
corresponding parts are congruent. We have 5
short cuts or methods.
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SSS
If we can show all 3 pairs of corr. sides are
congruent, the triangles have to be congruent.
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SAS
Show 2 pairs of sides and the included angles
are congruent and the triangles have to be
congruent.
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This is called a common side. It is a side for
both triangles.
Well use the reflexive property.
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Which method can be used to prove the triangles
are congruent
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Common side SSS
Vertical angles
SAS
Parallel lines alt int angles
Common side SAS
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PART 2
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ASA, AAS and HL
A
ASA 2 angles and the included side
S
A
AAS 2 angles and The non-included side
A
A
S
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HL ( hypotenuse leg ) is used only with right
triangles, BUT, not all right triangles.
ASA
HL
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PROOFS
When Starting A Proof, Make The Marks On The
Diagram Indicating The Congruent Parts. Use The
Given Info, Properties, Definitions, Etc.
Well Call Any Given Info That Does Not
Specifically State Congruency Or Equality A
PREREQUISITE
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SOME REASONS WELL 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

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Given AB BD EB BC Prove ?ABE
?DBC
A
C

B
1
2
Our Outline P rerequisites S ides A ngles S
ides Triangles
SAS
E
D

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A
C
Given AB BD EB BC Prove ?ABE
?DBC
B
1
2

SAS
E
D
STATEMENTS REASONS
none AB BD Given 1 2
Vertical angles EB BC
Given ?ABE ?DBC SAS
P S A S ?s

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C
Given CX bisects ACB A
B Prove ?ACX ?BCX

2
1

AAS
B
A
X
P A A S ?s
CX bisects ACB Given 1 2
Def of angle bisc A B
Given CX CX Reflexive
Prop ?ACX ?BCX AAS

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Can you prove these triangles are congruent?
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