Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Warm Up 9/29/081.Give the restrictions on the third side

of the triangle if the first two sides are 18 and 30.

2. Find x and y for both figures.

55° 70°x

y

100°2x + 104y

80

Math IDay 35 (9-29-08)

UNIT QUESTION: What are the properties and characteristics of polygons?Standard: MM1G1.e.

Today’s Question:What does it mean for two triangles to be congruent?Standard: MM1G.3.c.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Congruent triangles have congruent sides and congruent angles.

The parts of congruent triangles that “match” are called corresponding parts.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Complete each congruence statement.

CA

E

D

B

F

? ABC DEF

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

? ACB ECD

C

A

ED

B

Complete each congruence statement.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

? GHK GTK

KG

H

T

Complete each congruence statement.

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Corresponding Parts of Congruent Triangles are

Congruent

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Fill in the blanks

If CAT DOG, then A ___

because ________.

O

CPCTCC

A T

O

D

G

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Fill in the blanks

If FJH QRS, then ___ and F ___ because _______.Q CPCTC

J H RS

B CPCTCIf XYZ ABC, then ___ and Y ___ because _______.

ZX CA

Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

Overlapping sides are congruent in

each triangle by the REFLEXIVE property

Vertical Angles

are congruen

t

Alt Int Angles are congruent

given parallel

lines

Before we start…let’s get a few things straight

A B

C

X Z

Y

INCLUDED ANGLE

Side-Side-Side (SSS) Congruence Postulate

66

4 45 5

All Three sides in one triangle are congruent to all three sides

in the other triangle

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

Ex 1

statement. congruence a Write.

and , , trianglesIn two

UWDE

VWFEUVDF

DFE UVW

by ____SSS

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent.R

T

S

Y

X

Z

ΔRST ΔYZX by SSS

Ex 2

Not congruent.Not enough Information to Tell

R

TS

B

A C

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent.

Ex 3

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent.

Ex 4

R

P

S Q

ΔPQS ΔPRS by SAS

Determine iwhether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent.

Ex 5

R

P

S

Q

ΔPQR ΔSTU by SSS

T

U

Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent.

Ex 6

N

M

R

Not congruent.Not enough Information to Tell

Q

P

Before we start…let’s get a few things straight

INCLUDED SIDE

A B

C

X Z

Y

Angle-Side-Angle (ASA) Congruence Postulate

Two angles and the INCLUDED side

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

} Your Only Ways To Prove Triangles Are

Congruent

NO BAD WORDS

Ex 1

statement. congruence a Write.

and ,, and In

LE

NLDENDΔLMNΔDEF

DEF NLM

by ____ASA

Ex 2

What other pair of angles needs to be marked so that the two triangles are congruent by AAS?

F

D

E

M

L

N

NE

Ex 3

What other pair of angles needs to be marked so that the two triangles are congruent by ASA?

F

D

E

M

L

N

LD

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

ΔGIH ΔJIK by AAS

G

I

H J

KEx 4

ΔABC ΔEDC by ASA

B A

C

ED

Ex 5

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

ΔACB ΔECD by SASB

A

C

E

D

Ex 6

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

Not possible

K

J

L

T

U

Ex 7

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

V