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Warm UP!. Questions over HOMEWORK?. Skills check!. Congruence & Triangles. Congruent Triangles. Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts. S. Z. 60°. R. 50 °. 70°. T. Y. 2n+10°. X.

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slide4

Congruent Triangles

Congruent triangles have congruent sides and congruent angles.

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

rst is congruent to xyz find the value of n

S

Z

60°

R

50°

70°

T

Y

2n+10°

X

RST is congruent to XYZ. Find the value of n.

Since  RST is congruent to XYZ, the corresponding

parts are congruent.

60 = 2n+10

50 = 2n

n = 25

find the value of x if gfh ijk

G

J

Find the value of x if GFH  IJK.

x =11

K

100

F

45

(4x – 9)

I

H

slide11

Overlapping sides are congruent in each triangle by the REFLEXIVE property

Alt Int Angles are congruent given parallel lines

Vertical Angles are congruent

slide12

SSS

SAS

ASA

AAS

HL

The Only Ways To Prove Triangles Are Congruent

NO BAD WORDS

slide13

C

Y

A

B

X

Z

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

INCLUDED ANGLE

(an angle sandwich)

yum yum

slide14

C

Y

A

B

X

Z

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

INCLUDED SIDE

slide15

Side-Side-Side (SSS) Congruence Postulate

All Three SIDES of one triangle are congruent to all three sides of the other triangle

slide16

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

slide17

Angle-Side-Angle (ASA) Congruence Postulate

A

A

S

S

A

A

Two angles and the INCLUDED side

slide18

A

A

A

A

S

S

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

slide19

Congruent Right Triangles

HL

HYPOTENUSE AND LEG

slide20

On the following slides, we will determine if the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Then, state the postulate (rule) that you used to determine the congruency.

slide21

P

R

Q

S

ΔPQSΔPRS by SAS

slide22

P

S

U

Q

R

T

ΔPQRΔSTU by SSS

slide23

R

B

C

A

T

S

Not congruent.

Not enough Information to Tell

slide24

M

P

R

Q

N

Not congruent.

Not enough Information to Tell

slide25

G

K

I

H

J

ΔGIH ΔJIK by AAS

slide26

B

A

C

D

E

ΔABC ΔEDC by ASA

slide27

E

A

C

B

D

ΔACB ΔECD by SAS

slide28

J

T

L

K

V

U

Not possible

slide29

J

K

L

M

ΔMJK ΔLKM by SAS

slide30

J

K

U

L

ΔKJL ΔULM by HL

slide31

T

J

K

L

V

U

Not possible

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