Proving Triangles Congruent Free powerpoints at http www

Proving Triangles Congruent Free powerpoints at http: //www. worldofteaching. com

Corresponding Parts In Lesson 4. 1, 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

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

Do you need to show all sides and all angles? NO ! SSS SAS ASA AAS HL You can use 5 methods!

Side-Side (SSS) All three pairs of corresponding sides are congruent. H Q R G F 1. GH PQ 2. HF QR 3. GF PR P GHF PQR

Side-Angle-Side (SAS) Uses two sides and the included angle. B F E C A 1. BC FD 2. C D 3. AC ED D ABC EFD included angle

Included Angle The angle between two sides G I H

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

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

Included Side The side between two angles GI HI GH

Angle-Side-Angle (ASA) Uses two angles and the included side. B P N G H 1. G K 2. GB KP 3. B P K GBH KPN included side

Angle-Side (AAS) Uses two angles and a non-included side. C X T D M 1. D G 2. C X 3. CM XT G DMC GTX Non-included side

Hypotenuse-Leg (HL) • Needs a right triangle • Uses the hypotenuse and one other side (leg). 1. AC ZY (leg) ABC ZXY 2. AB ZX (hypotenuse) • To use hypotenuse-leg, you MUST have a right triangle!! • The hypotenuse is ALWAYS opposite the right angle.

Methods that DO NOT WORK! The following methods cannot be used to prove triangles congruent.

Warning: No A-S-S (“Donkey Theorem”) There is no such thing as an ASS (or 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

Not enough information Sometimes you won’t have enough information given to determine if 2 triangles are congruent.

The Congruence Postulates F SSS correspondence F ASA correspondence F SAS correspondence F ASS correspondence F AAA correspondence

Name That Postulate (when possible) SAS ASS Not ASA SSS

Name That Postulate (when possible) AAA SAS ASA ASS

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

HW: Name That Postulate (when possible) SSS No donkey theorem! ASS not allowed Not enough information AAA not allowed

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: