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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 :

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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.


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


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


Each pair of triangles is CONGRUENT. Do they show a Reflection, Translation, or Rotation?

reflection

translation

reflection

rotation

translation

reflection


REMEMBER…by definition…

Corresponding

Parts of

Congruent

Triangles are

Congruent


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