Triangle Congruence

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Triangle Congruence

• By Megan

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What is triangle congruence?

• Triangle congruence tells you if one triangle is
  congruent (or the same size and shape) of another
  triangle
• There are 6 different triangle situations and 4
  ways to tell if a triangle is congruent
• There are also 2 exceptions to the 4 triangle
  congruent theorems

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The 6 different triangle situations

• Congruent?
• YES
• YES
• YES
• YES
• NO
• NO

• Situation
• SSS
• SAS
• ASA
• AAS
• AAA
• SSA

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How can you tell if a triangle is congruent?

• There are 4 ways...
• Side, side, side (SSS) Congruence Theorem
• Angle, angle, side (AAS) Congruence Theorem
• Side, angle, side (SAS) Congruence Theorem
• Angle, side, angle (ASA) Congruence Theorem

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What do these theorems mean?

• SSS Congruence Theorem-
• If three sides of a triangle are congruent to
  three sides of another triangle, then the
  triangles are congruent.
• AAS Congruence Theorem-
• If two angles and the non-included side are
  congruent to the two angles and the non-included
  side of another triangle, then the two triangles
  are congruent.
• SAS Congruence Theorem-
• If two sides and the included angle are congruent
  to the two sides and included angle of another
  triangle, then the triangles are congruent.
• ASA Congruence Theorem-
• If two angles and the included side of one
  triangle is congruent to the two angles and
  included side of another triangle, then the
  triangles are congruent.

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What are the 2 exceptions to the triangle
congruence situations?

• The triangle situation SSA isnt congruent, but
  there are 2 exceptions
• If the triangle is a right triangle and you have
  the measures for the hypotenuse and the leg, then
  it is congruent and has a theorem
• If the triangle has one side bigger than the
  other and an angle, just like those of another
  triangle then theyre congruent and there is a
  theorem for it

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Theorems for the 2 triangle congruence exceptions

• Hypotenuse Leg Theorem (HL Theorem)
• In a right triangle, if the hypotenuse and one
  leg are congruent to the hypotenuse and one leg
  of another right triangle, then the triangles are
  congruent
• Side-small side-angle Congruence Theorem (SsA
  Congruence Theorem)
• If the two sides and the angle opposite the
  longer of the two sides in one triangle are
  congruent, respectively, to 2 sides and the
  corresponding angle in another triangle, than the
  triangles are congruent

7 cm
5 cm
90
5 cm
7 cm
90
E
ACgtBC
A
//
//
D
F
)
/
B
C
/
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Pictures of the 6 triangle situations
SSS
ASA
SAA
40
90
90
10 cm
10 cm
15 cm
5 cm
40
6 cm
SSA
SAS
AAA
90
20 cm
70
7 cm
30
90
20
7 cm
20 cm
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How can you use these theorems and situations?

• To complete mathematical proofs
• To tell if a triangle is congruent to another
  triangle without measuring
• To finish homework or other work quickly!!!
  Without guessing!!!

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• THE END!!!