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CONGRUENT

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sections 4-2, 4-3, 4-5 jim smith jchs some reasons we ll be using def of midpoint def of a bisector vert angles are congruent def of perpendicular bisector ... – PowerPoint PPT presentation

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Title: CONGRUENT


1
CONGRUENT TRIANGLES
Sections 4-2, 4-3, 4-5
Jim Smith JCHS
2
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
3
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.
4
SSS
If we can show all 3 pairs of corr. sides are
congruent, the triangles have to be congruent.
5
SAS
Show 2 pairs of sides and the included angles
are congruent and the triangles have to be
congruent.
6
This is called a common side. It is a side for
both triangles.
Well use the reflexive property.
7
Which method can be used to prove the triangles
are congruent
8
Common side SSS
Vertical angles
SAS
Parallel lines alt int angles
Common side SAS
9
PART 2
10
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
11
HL ( hypotenuse leg ) is used only with right
triangles, BUT, not all right triangles.
ASA
HL
12
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
13
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

14
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

15
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

16
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

17
Can you prove these triangles are congruent?
18
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19
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