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Proving Triangles Congruent. Free powerpoints at http://www.worldofteaching.com. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. How much do you need to know. . . . . . about two triangles
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Proving Triangles Congruent Free powerpoints at http://www.worldofteaching.com
F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape.
How much do you need to know. . . . . . about two triangles to prove that they are congruent?
Corresponding Parts • AB DE • BC EF • AC DF • A D • B E • C F B A C E F D In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF
SSS SAS ASA AAS Do you need all six ? NO !
Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF
Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle
Included Angle The angle between two sides H G I
E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y
Angle-Side-Angle (ASA) B E F A C D • A D • AB DE • B E ABC DEF included side
Included Side The side between two angles GI GH HI
E Y S Included Side Name the included side: Y and E E and S S and Y YE ES SY
Angle-Angle-Side (AAS) B E F A C D • A D • B E • 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
SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates
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 Property Vertical Angles SSA SAS
HW: Name That Postulate (when possible)
HW: Name That Postulate (when possible)
Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:
HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS: