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4-4 Proving Triangles Congruent by SSS and SAS - ÿ- ÿ ÿ) Co__qEqruence Postulate If three sides of one triangle are ÿ to three sides of a second triangle, then the two triangles are ÿ . B --€ If then 2 THINGS CAN BE ADDED TO A PICTURE IN A PROOF. YOUR PROOF MUST CONTAIN STEPS THAT SAY WHAT YOU ARE ADDING. Triangles that share a ÿ side. Since the same side is in both triangles, it can be marked ÿÿ:ÿ> REFLEXIVE PROPERTY . angles can be marked ÿ. Proof Blocks In Proof Blocks, every theorem, postulate, and definition is represented by a block. These blocks can either be physical manipulatives, or simply drawn on the page. ' Here is a link you can check out. http:llwww.proofblocks.comldetailsldetails/introduction.html 15 Example of Proof Blocks: Use SSS Congruence Postulate to Solve: Given: KL-ÿNL, KMÿMN N K Prove: DKLMÿ A NLM M i -- Picture Reflexive Property -- SSS ÿ, ÿN ,1ÿ ÿ Postulate How would this look as a 2-coulmn proof? i mÿiÿ: Use SSS Congruence Postulate to solve: Given: KLÿNL, KM ÿMN, Prove: A KLM ÿ A NLM Statements I, Kt %ÿt N K J KÿXÿ ÿN M 16 The angle formed by two adjacent sides of a polygon is called the ÿ ÿ1ÿ-ÿ. Draw an example of included angles: oÿ - ÿ- ÿ ÿ) Conqruence Postulate 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.. ÿ s If , then by ÿAÿ pÿrr.ÿ- _ÿ.[ÿ_ÿÿ) Conqruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the two triangles are congruent. A D Reme.mbÿr Rieht ÿldOngleÿ: E , then 17 Example: Use 5AS Postulate to solve. B Given: BC z AD & BC //AD Prove: zÿABC ÿACDA Statements e ÿ C Reasons A e b, 18