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CONGRUENT TRIANGLES. Sections 4-2, 4-3, 4-5. Jim Smith JCHS. Warm Up. What is the same in these two triangles?. 30. 30. 80. 70. When we talk about congruent triangles, we mean everything about them Is congruent. All 3 pairs of corresponding angles are equal…. A. D. E.

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Presentation Transcript
slide1

CONGRUENT

TRIANGLES

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

Jim Smith JCHS

slide2

Warm Up

What is the same in these two triangles?

30

30

80

70

slide3

When we talk about congruent triangles,

we mean everything about them Is congruent.

All 3 pairs of corresponding angles are equal….

A

D

E

C

F

B

And all 3 pairs of corresponding sides are equal

Name the corresponding parts:

slide4

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.

slide5

SSS

If we can show all 3 pairs of corr.

sides are congruent, the triangles

have to be congruent.

slide6

SAS

Non-included

angles

Included

angle

Show 2 pairs of sides and the

included angles are congruent and

the triangles have to be congruent.

slide7

This is called a common side.

It is a side for both triangles.

We’ll use the reflexive property.

slide8

Which method can be used to

prove the triangles are congruent

slide9

Common side

SSS

Vertical angles

SAS

Parallel lines

alt int angles

Common side

SAS

slide11

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

slide12

HL ( hypotenuse leg ) is used

only with right triangles, BUT,

not all right triangles.

ASA

HL

slide13

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
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
slide15

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

=

slide16

A

C

Given: AB = BD

EB = BC

Prove: ∆ABE ˜ ∆DBC

B

1

2

=

SAS

E

D

STATEMENTS REASONS

P

S

A

S

∆’s

none

AB = BD Given

1 = 2 Vertical angles

EB = BC Given

∆ABE ˜ ∆DBC SAS

=

slide17

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

=

slide18

Team Challenge!

We have seven problems. We will be in teams and the team who scores the most points will get a prize!

The Rules:

I will pose a question and the first team to write the correct answer on their side of the board gets first chance to earn the point.

I will select a member of the team to explain how they got the correct answer to earn their team a point. Who will I call on?... YOU! 

slide21

E

B

D

F

A

C

slide22

B

E

C

A

D

slide23

B

A

C

D

slide24

C

B

D

E

A

slide25

Which two triangles are congruent and how?

C

D

30⁰

B

20⁰

10⁰

E

A

Ticket out the door! (Graded)