Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6...

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Triangle Congruence

Transcript of Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6...

Page 1: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

TriangleCongruence

Page 2: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Define congruent….Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Page 3: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

IN ORDER FOR TWO TRIANGLES TO BE CONGRUENT ALL

CORRESPONDING ANGLES AND SIDES MUST BE CONGRUENT!

Congruency StatementΔABC≅ΔDEF

Based on the congruency statement, which angles and which sides must be congruent?

Page 4: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Complete the congruency statement for the following

triangles…ΔPQR≅Δ_______________ ΔPQR≅Δ_______________

Page 5: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Name the corresponding congruent parts for these triangles.

Corresponding Parts

ABC DEF

B

A C

E

D

F

1. AB 2. BC 3. AC 4. A 5. B 6. C

Page 6: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Do you need all six ?

NO !

SSSSASASAAAS

Page 7: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Side-Side-Side (SSS)

1. AB DE

2. BC EF

3. AC DF

ABC DEF

B

A

C

E

D

F

If three sides of one triangle are congruent to three corresponding sidesof a second triangle, then the triangles are congruent.

Page 8: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

http://www.youtube.com/watch?v=o009kN8bCC8

COMERCIAL BREAK!!!

Page 9: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

The angle between two sides

Included Angle

G I H

Page 10: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Name the included angle:

YE and ES

ES and YS

YS and YE

Included Angle

SY

E

E

S

Y

The included angle is the angle with the letter that both sides share

Page 11: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Side-Angle-Side (SAS)

1. AB DE

2. A D

3. AC DF

ABC DEF

B

A

C

E

D

F

included angle

If two sides of one triangle and the included angle are congruent the two corresponding sides and included angle, then the triangles are congruent.

Page 12: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

http://www.youtube.com/watch?v=4GZtALwvRaE&feature=grec_index

COMERCIAL BREAK!!!

Page 13: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

The side between two angles

Included Side

GI HI GH

Page 14: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Name the included angle:

Y and E

E and S

S and Y

Included Side

SY

E

YE

ES

SY

Page 15: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Angle-Side-Angle (ASA)

1. A D2. AB DE

3. B E

ABC DEF

B

A

C

E

D

F

included side

If two angles of a triangle and the included side are congruent the corresponding angles and included side, then the triangles are congruent.

Page 16: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Angle-Angle-Side (AAS)

1. A D

2. B E

3. BC EF

ABC DEF

B

A

C

E

D

F

Non-included

side

If two angles of a triangle and the non-included side are congruent the corresponding angles and non-included side, then the triangles are congruent.

Page 17: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Side Names of Triangles

• Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs.

leg

leg

hypotenuse

Page 18: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Examples: Tell whether the segment is a leg or a

hypotenuse.

Page 19: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Hypotenuse- Leg (HL) Congruence Theorem:

• If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

• Example: because of HL.XYZABC A X

B C Y Z

Page 20: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Examples: Determine if the triangles are congruent. State

the postulate or theorem.

Page 21: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

There are 5 ways to prove triangles are congruent…

• Each of these ways have 3 things to look for!– ASA– SAS– SSS– AAS– HL (Right Triangle)

Page 22: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Warning: No ASS or SSA PostulateNO CURSING IN MATH CLASS!

A C

B

D

E

F

NOT CONGRUENT

There is no such thing as an SSA

postulate!

Page 23: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Warning: No AAA Postulate

A C

B

D

E

F

There is no such thing as an AAA

postulate!

NOT CONGRUENT

Page 24: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

The Congruence Postulates

SSS correspondence

ASA correspondence

SAS correspondence

AAS correspondence

HL correspondence

SSA correspondence

AAA correspondence

Page 25: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

http://www.youtube.com/watch?v=hQYfCWak-Q0

COMERCIAL BREAK!!!

Page 26: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Name That Postulate

SASASA

SSSSSA

(when possible)

Page 27: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Name That Postulate(when possible)

ASA

SAS

AAA

SSA

Page 28: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Name That Postulate(when possible)

SAS

SAS

SAS

Reflexive Property

Vertical Angles

Vertical Angles

Reflexive Property SS

A

Page 29: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

You try! Name That Postulate(when possible)

Page 30: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

(when possible)You try! Name That Postulate

Page 31: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

Let’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

B D

For AAS: A F

AC FE

Page 32: Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

You Try!Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

For AAS: