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# Section 3.1 PowerPoint PPT Presentation

Section 3.1. What Are Congruent Figures?. D. A. B. F. C. E. 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 corresponding congruent parts :

Section 3.1

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## Section 3.1

What Are Congruent Figures?

D

A

B

F

C

E

### 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 corresponding

congruent parts:

• congruent angles

• congruent segments

And therefore…

S

R

X

Y

Z

T

### CongruentTriangles

• Congruent triangles

• If all pairs of corresponding parts are congruent, then

Parallelogram ABCDParallelogram PQRS

### Vocabulary

• Congruent Polygons

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

P

A

Q

D

B

S

R

C

### Caution

• 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

and

### 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

Reflexive Property (Postulate)

Any figure or segment is congruent to itself

F

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

FGH

FIH ?

G

I

### Reflexive Property

H

What property could we use to show this is true?

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

### Hints for finding congruent parts…

Try and find out if your triangles are

• Reflections or Flips

• Translations or Slides

• Rotations or Turns

B

A

C

### Reflection (or Flip)

A figure has been reflected if it has been flipped over a line.

E

D

F

S

O

P

L

@

@

@

@

LM

PQ

LO

PS

ON

SR

MN

QR

M

N

Q

R

### Translation (or Slide)

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

K

J

J

K

### 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.

F

G

L

reflection

translation

reflection

rotation

translation

reflection

Corresponding

Parts of

Congruent

Triangles are

Congruent