Warm UP!

1 / 32

# Warm UP! - PowerPoint PPT Presentation

Warm UP!. Questions over HOMEWORK?. Skills check!. Congruence &amp; 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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Warm UP!' - emily-jenkins

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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

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

G

J

Find the value of x if GFH  IJK.

x =11

K

100

F

45

(4x – 9)

I

H

Overlapping sides are congruent in each triangle by the REFLEXIVE property

Alt Int Angles are congruent given parallel lines

Vertical Angles are congruent

SSS

SAS

ASA

AAS

HL

The Only Ways To Prove Triangles Are Congruent

C

Y

A

B

X

Z

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

INCLUDED ANGLE

(an angle sandwich)

yum yum

C

Y

A

B

X

Z

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

INCLUDED SIDE

Side-Side-Side (SSS) Congruence Postulate

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

Side-Angle-Side (SAS) Congruence Postulate

Two sides and the INCLUDED angle

Angle-Side-Angle (ASA) Congruence Postulate

A

A

S

S

A

A

Two angles and the INCLUDED side

A

A

A

A

S

S

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

Congruent Right Triangles

HL

HYPOTENUSE AND LEG

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.

P

R

Q

S

ΔPQSΔPRS by SAS

P

S

U

Q

R

T

ΔPQRΔSTU by SSS

R

B

C

A

T

S

Not congruent.

Not enough Information to Tell

M

P

R

Q

N

Not congruent.

Not enough Information to Tell

G

K

I

H

J

ΔGIH ΔJIK by AAS

B

A

C

D

E

ΔABC ΔEDC by ASA

E

A

C

B

D

ΔACB ΔECD by SAS

J

T

L

K

V

U

Not possible

J

K

L

M

ΔMJK ΔLKM by SAS

J

K

U

L

ΔKJL ΔULM by HL

T

J

K

L

V

U

Not possible