4.4+Proving+Triangles+Congruent+ASA,+AAS

=Goals of this Chapter:= 1. Prove that triangles are congruent using the ASA Congruence Postulate and the AAS Congruence Theorem. 2. Use congruence postulates and theorems in **real-life** problems (Online Pg. 220)

My Summary:

 * The whole chapter is a lesson on understanding ASA Postulate and AAS Theorem, both are very helpful in determining whether or not triangles are congruent. The Postulate and Theorem are also used for Proofs, which were introduced in previous chapters, however in Chapter 4 the proofs are taken one step further with ASA and AAS. **

** Angle-Side-Angle (ASA) Congruence Postulate **   If two angles + the included side of one triangle are congruent to two angles + included side of a second triangle= two triangles are congruent.

(Picture-Pg. 220) 

By the Third Angles Theorem, the third angles are also congruent.
====That is, B E. Notice that  is the side included between B and C, and  is the side included between E and F. You can apply the ASA Congruence Postulate to conclude that ΔABC  ΔDEF.====

Sample Proofs:
Example 1:

(Proof Example- Pg 221)
Example 2:

Given: ∠A ≅ ∠D, ∠C ≅ ∠F, BC ≅ EF Prove: ∆ABC ≅ ∆DEF

Paragraph Proof: You are given that two angles of ∆ABC are congruent to two angles of ∆DEF. By the Third Angles Theorem, the third angles are also congruent. That is, ∠B ≅ ∠E. Notice that BC is the side included between ∠B and ∠C, and EF is the side included between ∠E and ∠F. You can apply the ASA Congruence Postulate to conclude that ∆ABC ≅ ∆DEF.

(http://www.myteacherpages.com/webpages/rrandolph/resources.cfm?subpage=468379 powerpoint) = = =Practice Problems:=

Try doing some proofs all on your own!

http://www.myteacherpages.com/webpages/rrandolph/resources.cfm?subpage=479444 Click on the Word file and there are a bunch of practice problems

http://regentsprep.org/regents/mathb/1b/Reccontri.htm This website has practice problems that include properties- SAS, ASA, SSS, AAS, HL

http://regentsprep.org/Regents/mathb/1c/preprooftriangles.htm This website has problems that allow you to do actual two-column proofs. It's very helpful.