Proving Triangles Congruent

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

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

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

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

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

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

Included Angle The angle between two sides G I H

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

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

Included Side The side between two angles GI HI GH

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

Angle-Side (AAS) B E F A C 1. A D 2. B E D ABC DEF 3. BC EF Non-included side

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

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

The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F AAS correspondence F SSA correspondence F AAA correspondence

Name That Postulate (when possible) SAS SSA ASA SSS

Name That Postulate (when possible) AAA SAS ASA SSA

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

HW: Name That Postulate (when possible)

HW: Name That Postulate (when possible)

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

HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

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