Proving Triangles Congruent

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Proving Triangles Congruent

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Presentation transcript:

Proving Triangles Congruent jc-schools.net/PPT/geometrycongruence.ppt

The Idea of a Congruence Two geometric figures with exactly the same size and shape. A C B D E F jc-schools.net/PPT/geometrycongruence.ppt

How much do you need to know. . . . . . about two triangles to prove that they are congruent? jc-schools.net/PPT/geometrycongruence.ppt

Reflexive Property of Congruence A segment is congruent to itself. An angle is congruent to itself.

Side-Side-Side (SSS) Postulate 8-1: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF B E F A C D jc-schools.net/PPT/geometrycongruence.ppt

Side-Angle-Side (SAS) Postulate 8-2: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) B E F A C D AB  DE A   D AC  DF ABC   DEF included angle jc-schools.net/PPT/geometrycongruence.ppt

Included Angle The angle between two sides  H  G  I jc-schools.net/PPT/geometrycongruence.ppt

Included Angle Name the included angle: YE and ES ES and YS YS and YE jc-schools.net/PPT/geometrycongruence.ppt

Included Side The side between two angles GI GH HI jc-schools.net/PPT/geometrycongruence.ppt

Included Side Name the included angle: Y and E E and S S and Y YE ES SY jc-schools.net/PPT/geometrycongruence.ppt

How are the triangles congruent? Vertical Angles Reflexive Property SAS SAS Vertical Angles SAS jc-schools.net/PPT/geometrycongruence.ppt

Homework Work Packet: SSS and SAS