4.4 Proving Triangles Congruent- SSS, SAS Then: You proved triangles congruent using the definition of congruence. Now: 1. Use the SSS Postulate to test for triangle congruence. 2. Use the SAS Postulate to test for triangle congruence. http://www.southallegheny.org/webpages/trishel/photos/x_013400_bridge.jpg

Review: Write a congruence statement for the triangles: How do you know that the triangles are congruent? http://www.tutornext.com/system/files/u19/Congruent_triangles.gif

Postulate 4.1: Side-Side-Side (SSS) Congruence If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If Side AB  ______, Side BC  ______, and Side AC  ______. Then ABC   ________

Example 1: Use SSS to prove triangles congruent a. Given: FJ  HJ, G is the midpoint of FH. Prove: FGJ  HGJ 1. It is given that FJ  ________. 2. Point G is the midpoint of FH, so _____________. 3. By the Reflexive Property, __________________. 4. By the ___________________________, FGJ  HGJ.

Example 1: Use SSS to prove triangles congruent b. Given: RS  UT, RT  US Prove: RST  UTS Statements Reasons 1. RS  UT, RT  US 1. _______________ 2. ST  TS 2. _______________ 3. RST  UTS 3. _______________

Example 2: SSS on the coordinate plane DFG has vertices D(-2,4), F(4,4), and G(-2,2). LMN has vertices L(-3,-3), M(-3,3) and N(-1,-3). Graph the triangles in the same coordinate plane and show that they are congruent. If sides are vertical or horizontal, count spaces. If not, use distance formula:  (x2 – x1)2 + (y2 – y1)2

Example 2 continued DF = DG = GF = ML = LN = MN = ____________ ______________ by _______________________________

Postulate 4.2: Side-Angle-Side (SAS) Congruence If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If Side RT  ______, Angle R  ______, and Side RS  ______, Then  RST   ________

Example 3: Use SAS to prove triangles congruent a. Given: V is the midpoint of YZ V is the midpoint of WX. Prove:  XVZ  WVY 1. Since V is the midpoint of YZ and WX, __________ _______________________________________. 2. Since YVW and XVZ are __________________ _______________________________________ 3. Therefore, by _________________, _____ ____

Example 3: Use SAS to prove triangles congruent b. Given: AB = CD, AB  CD Prove: DBA  ACD Statements Reasons 1. AB = CD, AB  CD 1. _________________ 2. DAB  ADC 2. _________________ 3. AD = AD 3. _________________ 4.  DBA  ACD 4. _________________

Example 4: Use SSS or SAS For each diagram, determine which pairs of triangles can be proved congruent. a. b. c. d.

4.4 Assignment p. 269-272- #5, 6,12-15 and 24 are proofs on handout. #8 and #10- graph and use distance formula for all sides that are not vertical or horizontal. #16-19, 27, 28, and 30 on own paper or on graph paper.