4.4 Isosceles Triangles, Corollaries, & CPCTC. ♥Has at least 2 congruent sides. ♥The angles opposite the congruent sides are congruent ♥Converse is also.

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Presentation transcript:

4.4 Isosceles Triangles, Corollaries, & CPCTC

♥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. Isosceles Triangles

♥The bisector of the vertex angle of an isosceles Δ is the perpendicular bisector of the base. Vertex angle In addition, you just learned that the angles opposite congruent sides are congruent… Base

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 . A C B G E F That means that EG  CB What is AC congruent to? FE

Corresponding parts of congruent triangles are congruent.

If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent. Corresponding Parts of Congruent Triangles are Congruent. You can only use CPCTC in a proof AFTER you have proved congruence. CPCTC

For example: Prove: AB  DE A FE D C B Statements Reasons AC  DF Given  C   F Given CB  FE Given ΔABC  ΔDEF SAS AB  DE CPCTC

Your assignment 2 - Cut and paste proofs 2 – DIY proofs 3 - Constructions