Proving Triangles Congruent

Two geometric figures with exactly the same size and shape. The Idea of a Congruence A C B DE F

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 HL ASA AAS

Side-Side-Side (SSS) 1. AB  DE 2. BC  EF 3. AC  DF  ABC   DEF C B A E D F

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

Hypotenuse Leg (HL) 1. AB  DE 2.  B   E 3. AC  DF  ABC   DEF B A C E D F right angle

Angle-Side- Angle (ASA) 1.  A   D 2. AB  DE 3.  B   E  ABC   DEF B A C E D F included side

The side between two angles Included Side GI HI GH

Name the included side:  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

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

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

The Congruence Postulates  SSS  SAS  HL  ASA  AAS  SSA or ASS  AAA

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) Reflexive Property SSS none SSA AAA

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

Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS:  B   D For AAS: A  F A  F AC  FE

Try it! Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:  N   V MK  TU  M   U

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