What Are Congruent Figures

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Section 3.1

• What Are Congruent Figures?

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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
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Congruent Triangles

• Congruent triangles
• If all pairs of corresponding parts are
  congruent, then

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Vocabulary

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

P
A
Q
D
B
S
R
C
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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
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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

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Reflexive Property

• Reflexive Property (Postulate)

• Any figure or segment is congruent to itself

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.
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Based on the markings on these triangles, NAME
the congruent triangles correctly.
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Hints for finding congruent parts

• Try and find out if your triangles are
• Reflections or Flips
• Translations or Slides
• Rotations or Turns

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Reflection (or Flip)
A figure has been reflected if it has been
flipped over a line.
E
D
F
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Translation (or Slide)

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

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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
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Each pair of triangles is CONGRUENT. Do they
show a Reflection, Translation, or Rotation?
reflection
reflection
translation
translation
rotation
reflection
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REMEMBERby definition

• Corresponding
• Parts of
• Congruent
• Triangles are
• Congruent