Proving Triangles Congruent

How much do you need to know... need to know about two triangles to prove that they are congruent?

you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Corresponding Parts  ABC   DEF B A C E D F 1.AB  DE 2.BC  EF 3.AC  DF 4.  A   D 5.  B   E 6.  C   F

Do you need all six ? NO ! SSS SAS ASA AAS

Side-Side-Side (SSS) 1. AB  DE 2. BC  EF 3. AC  DF  ABC   DEF B A C E D F If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent

Side-Angle-Side (SAS) 1. AB  DE 2.  A   D 3. AC  DF  ABC   DEF B A C E D F 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 included angle

The angle between two sides Included Angle  G G  I I  H H

Name the included angle: YE and ES ES and YS YS and YE Included Angle SY E  E E  S S  Y Y

Angle-Side- Angle (ASA) 1.  A   D 2. AB  DE 3.  B   E  ABC   DEF B A C E D F included side If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The side between two angles Included Side GI HI GH

Name the included angle:  Y and  E  E and  S  S and  Y Included Side SY E YE ES SY

Angle-Angle-Side (AAS) 1.  A   D 2.  B   E 3. BC  EF  ABC   DEF B A C E D F Non-included side If 2 angles and a non-included side of 1 triangle are congruent to 2 angles and the corresponding non- included side of another triangle, then the 2 triangles are congruent

Warning: No SSA Postulate A C B D E F NOT CONGRUENT There is no such thing as an SSA postulate!

Warning: No AAA Postulate A C B D E F There is no such thing as an AAA postulate! NOT CONGRUENT

Name That Postulate SAS ASA SSS SSA (when possible)

Name That Postulate (when possible) ASA SAS AAA SSA

Name That Postulate (when possible) SAS SAS SAS Reflexive Property Vertical Angles Reflexive Property SSA

Name That Postulate (when possible)

HW: Name That Postulate

Let’s Practice Indicate the additional information needed to enable us to prove the triangles are congruent. For SAS: For ASA:  B   D For AAS: A  F A  F AC  FE