4.4 Isosceles Triangles, Corollaries,

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4.4 Isosceles Triangles,Corollaries, CPCTC
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Isosceles Triangles

• Has at least 2 congruent sides.
• The angles opposite the congruent sides are
  congruent
• Converse is also true. The sides opposite the
  congruent angles are also congruent.
• This is a COROLLARY.
• A corollary naturally follows a theorem or
  postulate. We can prove it if we need to, but it
  really makes a lot of sense.

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• The bisector of the vertex angle of an isosceles
  ? is the perpendicular bisector of the base.

In addition, you just learned that the angles
opposite congruent sides are congruent
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Corresponding parts

• When you use a shortcut (SSS, AAS, SAS, ASA, HL)
  to show that 2 triangles are ?,
• that means that ALL the corresponding parts are
  congruent.
• EX If a triangle is congruent by ASA (for
  instance), then all the other corresponding parts
  are ?.

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Corresponding parts of congruent triangles are
congruent.
Corresponding parts of congruent triangles are
congruent.
Corresponding parts of congruent triangles are
congruent.
Corresponding parts of congruent triangles are
congruent.
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Corresponding Parts of Congruent Triangles are
Congruent.
CPCTC

• If you can prove congruence using a shortcut,
  then you KNOW that the remaining corresponding
  parts are congruent.

You can only use CPCTC in a proof AFTER you have
proved congruence.
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For example
A

• Prove AB ? DE

B
C
D
F
E
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Your assignment

• 2 - Cut and paste proofs
• 2 DIY proofs
• 3 - Constructions