Congruence Problems Using the theorems

Congruency Thms. SSS ASA SAS RHS (or AAS) x List the 4 triangle congruency thms. Hypotenuse SSS ASA (or AAS) SAS RHS

-Consider this- SAS Why are the two triangles congruent? D What are the corresponding vertices? What are the corresponding sides? A B C D E F SAS A   D C   E B   F

-Example 1- G Draw a triangle GHI in which: 6 cm I mG = 90° mG= 90°, 30° mH = 30° mH = 30°. H Will everyone else’s drawing be congruent to yours? Why or why not?

-Example 2- SSS A reflection Why are the two triangles congruent? Name the corresponding vertices What isometry maps ADB onto CDB? A SSS D B A   C ADB   CDB ABD   CBD C A reflection

-Example 3- S A S A Given: A is a midpoint of Prove: BAE   DAC. A is midpoint of BD BAE  DAC Vert. opposite angles A is midpoint of EC  BAE  DAC By SAS property

-Example 4- S S Given: Prove: B  D      ABC  CDA  B  D Reflexive property  ABC  CDA By SSS property      B  D Corresponding ’s in congruent ’s are congruent

-Example 5- R R H H S S Given: Prove:    mQSR = mPRS = 90° T Given: mQSR = mPRS = 90° Prove: QSR  PRS = 90° R H S R H S Given Given Reflexive property  QSR  PRS By RHS property    Corresponding sides in congruent ’s are congruent