Understanding Triangle Congruence Proofs
Exploring the concept of proving triangles congruent, this content covers the different criteria such as SAS, SSS, ASA, AAS, and the warning against using the SSA postulate. Corresponding parts, included angles, and sides, along with visual aids, help grasp the key principles to demonstrate triangle congruence.
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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. 1. AB DE 2. BC EF 3. AC DF 4. A D 5. B E 6. C F ABC DEF
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
Side-Angle-Side (SAS) 1. AB DE 2. A D 3. AC DF ABC DEF included angle
Included Angle The angle between two sides H G I
Included Angle Name the included angle: E YE and ES ES and YS YS and YE E S Y Y S
Angle-Side-Angle (ASA) 1. A D 2. AB DE 3. B E ABC DEF include d side
Included Side The side between two angles GI GH HI
Included Side Name the included angle: E Y and E E and S S and Y YE ES SY Y S
Angle-Angle-Side (AAS) 1. A D 2. B E 3. BC EF ABC DEF 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 F D NOT CONGRUENT
The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence
Name That Postulate (when possible) SAS ASA SSA SSS
Name That Postulate (when possible) AAA ASA SSA SAS
Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive PropertySSA Vertical Angles SAS
HW: Name That Postulate (when possible)
HW: Name That Postulate (when possible)
Lets Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. B D AC FE For ASA: For SAS: A F For AAS:
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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