Isosceles Triangles, Corollaries, & CPCTC

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Presentation transcript:

Isosceles Triangles, Corollaries, & CPCTC

Corresponding parts of congruent triangles are congruent.

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.

Corresponding parts When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are congruent, 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 congruent. A C B G E F That means that EG  CB FE What is AC congruent to?

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

Get: a piece of patty paper a straight edge your pencil your compass We are going to create an isosceles triangles with 2 congruent sides.

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.

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

Your assignment 4.4 Practice Worksheet 4.5 Practice Worksheet