Section 3.1

What Are Congruent Figures?

D

EF

Congruent Figures A non-geometry student may describe

CONGRUENT triangles as having the same size and shape

A geometry student would describe them as having 6 pairs of correspondingcongruent parts:◦ congruent angles ◦ congruent segments

A

B C

AB DF AC DE BC FEA D B F C E

ABC DFEAnd therefore…

Congruent Triangles Congruent triangles

If all pairs of corresponding parts are congruent, then

X

Y Z

S

T

R

X T Y R Z S

XY TR YZ RS XZ TS

XYZ TRS

Vocabulary Congruent Polygons

All pairs of corresponding parts (angles and sides) are congruent.

, , , A B CP Q R SD

A

BC

DP

R

Q

S

Parallelogram ABCD Parallelogram PQRS, , , and AB BC CDPQ QR RS SPDA

Caution

B

B C Y Z

A C X Z

B A Y XZ

Y

C

A X

A XBC ZY Be careful when naming congruent figures, corresponding parts must be listed in the same order To check this, match up

the vertices of the corresponding angles.

This notation means that

C

AB Y

B Y

Z

X

X

Z

CA

and

X

Y ZC

B A

X

Y ZC

B A

Caution

Sometimes it is difficult to tell what parts of a congruent figure are congruent.

To keep from making mistakes: Label your congruent

sides and angles with tick marks

and/or Use colored pencils

A XBC ZY

X

Y ZC

B A

X

Y ZC

B A

Reflexive Property Reflexive Property

(Postulate) Any figure or segment

is congruent to itself

HI

F

G

Given the diagram as shown, what else do you need to know in order to say that

FGH FIH ?

FHFH

What property could we use to show this is true?

The reflexive property, it says that any figure or segment is congruent to itself.

Based on the markings on these triangles, NAME the congruent triangles correctly.

OKL PMN MAT HTA

WVY WXZ

PO

NMK L

43

D

CB

A

Z

Y

XWV

H

TA

M

BAD BCD

Hints for finding congruent parts…

Try and find out if your triangles are

ReflectionsReflections or or FlipsFlipsTranslationsTranslations or or SlidesSlidesRotationsRotations or or TurnsTurns

Reflection (or Flip) A figure has been reflected if it has been

flipped over a line.

C

A

B

D

F

E

AB DE AC DF BC EF

A D B E C F

ABC DEF

Translation (or Slide)

The two figures shown are congruent. The correspondence is evident if we slide or translate one onto the other.

P

Q R

S

L

M N

O

L P M Q N R O S

LMNO PQRS

LM PQ LO PS ON SR MN QR

Rotation (or turn)

A figure that has been rotated has been turned to form a congruent figure. Sometimes it is easier to see the corresponding parts if we rotate one onto the other.

L

F

GJ

K

J

K

FL KL FG KJ GL JL

L L F K G J

KLJ FLG

Each pair of triangles is CONGRUENT. Do they show a ReflectionReflection, , TranslationTranslation, or RotationRotation?

12117

8

3 4

10

1

25 6

9

1

reflection

reflection

translation

translation

rotation

reflection

REMEMBER…by definition…

Corresponding Parts of Congruent Triangles areCongruent