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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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Warm up

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



Warm up

Overlapping sides are congruent in each triangle by the REFLEXIVE property

Alt Int Angles are congruent given parallel lines

Vertical Angles are congruent


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SSS REFLEXIVE property

SAS

ASA

AAS

HL

The Only Ways To Prove Triangles Are Congruent

NO BAD WORDS


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C REFLEXIVE property

Y

A

B

X

Z

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

INCLUDED ANGLE

(an angle sandwich)

yum yum


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C REFLEXIVE property

Y

A

B

X

Z

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

INCLUDED SIDE


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Side-Side-Side (SSS) Congruence Postulate REFLEXIVE property

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


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Side-Angle-Side (SAS) Congruence Postulate REFLEXIVE property

Two sides and the INCLUDED angle


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Angle-Side-Angle (ASA) Congruence Postulate REFLEXIVE property

A

A

S

S

A

A

Two angles and the INCLUDED side


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A REFLEXIVE property

A

A

A

S

S

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included


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Congruent Right Triangles REFLEXIVE property

HL

HYPOTENUSE AND LEG


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On the following slides, we will d REFLEXIVE propertyetermine 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.


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P REFLEXIVE property

R

Q

S

ΔPQSΔPRS by SAS


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P REFLEXIVE property

S

U

Q

R

T

ΔPQRΔSTU by SSS


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R REFLEXIVE property

B

C

A

T

S

Not congruent.

Not enough Information to Tell


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M REFLEXIVE property

P

R

Q

N

Not congruent.

Not enough Information to Tell


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G REFLEXIVE property

K

I

H

J

ΔGIH ΔJIK by AAS


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B REFLEXIVE property

A

C

D

E

ΔABC ΔEDC by ASA


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E REFLEXIVE property

A

C

B

D

ΔACB ΔECD by SAS


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J REFLEXIVE property

T

L

K

V

U

Not possible


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J REFLEXIVE property

K

L

M

ΔMJK ΔLKM by SAS


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J REFLEXIVE property

K

U

L

ΔKJL ΔULM by HL


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T REFLEXIVE property

J

K

L

V

U

Not possible


Practice
Practice REFLEXIVE property