Proving Triangles Congruent www assignmentpoint com The Idea

Proving Triangles Congruent www. assignmentpoint. com

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

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

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 A C ABC DEF 5. B E E 6. C F F D www. assignmentpoint. com

Do you need all six ? NO ! www. assignmentpoint. com SSS SAS ASA AAS

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

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

Included Angle The angle between two sides G I www. assignmentpoint. com H

Included Angle Name the included angle: E Y S YE and ES E ES and YS S YS and YE Y www. assignmentpoint. com

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

Included Side The side between two angles GI HI www. assignmentpoint. com GH

Included Side Name the included angle: E Y S Y and E YE E and S ES S and Y SY www. assignmentpoint. com

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

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

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

The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F AAS correspondence F SSA correspondence F AAA correspondence www. assignmentpoint. com

Name That Postulate (when possible) SAS ASA SSS www. assignmentpoint. com

Name That Postulate (when possible) AAA ASA SAS www. assignmentpoint. com

Name That Postulate (when possible) Reflexive Property SAS Vertical Angles SAS Reflexive SAS Property www. assignmentpoint. com SSA

HW: Name That Postulate (when possible) www. assignmentpoint. com

HW: Name That Postulate (when possible) www. assignmentpoint. com

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 www. assignmentpoint. com

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