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CONGRUENT TRIANGLES

Sections 4-2, 4-3, 4-5

Jim Smith JCHS

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 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.

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.

This is called a common side. It is a side for

both triangles.

Well use the reflexive property.

Which method can be used to prove the triangles

are congruent

Common side SSS

Vertical angles

SAS

Parallel lines alt int angles

Common side SAS

PART 2

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

HL ( hypotenuse leg ) is used only with right

triangles, BUT, not all right triangles.

ASA

HL

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

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

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

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

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

Can you prove these triangles are congruent?

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