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The Fast Food Factory Sandwich Shop by Mrs. Bentz FMHS YUM! Which sandwich is good to eat? SSS = Spicy Summer Sausage AKA: Side Side Side (SSS) 3 pairs of Congruent Sides By definition of a triangle: If you have three congruent pairs of sides, you must have 3 pairs of congruent angles. #1 SSS If 3 sides of 1 triangle are congruent to 3 sides of another triangle, then the two triangles are congruent. S 1.5in S 1.5in 2in S 2in S S 3in S 3in Awesome Authentic Anchovy AKA: Angle Angle Angle (AAA) 3 pairs of congruent angles Do they have to all be the same size? #2 AAA If 3 angles of 1 triangle are congruent to 3 angles of another triangle, then the triangles are similar but not necessarily congruent A 100° A 100° 50° A 50° 30° A A 30° A Succulent Aromatic Swine • AKA: Side Angle Side (SAS) • The angle is “sandwiched” between the two sides Oink #3 SAS S If two sides and the included angle of 1 triangle are congruent to the 2 sides and included angle of another triangle, then the two triangles are congruent. S 2in 2in 50° A 5 in S 50° A 5 in S Super Sized Antelope • AKA: Side Side Angle (SSA) • Watch out! We don’t allow bad words in Geometry land…. #4 SSA Does not prove triangles are congruent A A A 40° S 40° 2 in S 2 in S 2 in 1.5 in S 1.5 in S 1.5 in S 40° Appetizing Sesame Avocado AKA: Angle Side Angle (ASA) The side is “sandwiched” between two angles #5 ASA If 2 angles and the included side of 1 triangle are congruent to the 2 angles and included side of another triangle, then the 2 triangles are congruent. 40° A 40° 70° A 70° 2.5 in S A 2.5 in S A Aunt Annie’s Steak ► AKA: Angle Angle Side (AAS) ► Not the “sandwiched” side ► Can be either of the two sides #6 AAS • If 2 angles and a side of 1 triangle are congruent to 2 angles and a side of another triangle, then the 2 triangles are congruent A A A 95° A 47° 1.8 in S 95° 47° 1.8 in S Heaping Left-overs AKA: Hypotenuse Leg You must have two right triangles to use this theorem Helps us not say the bad word #7 HL In a right triangle, if the hypotenuse and leg of one triangle are congruent to the hypotenuse and leg of another triangle, then the triangles are congruent. 3 in 1.5 in L H 3 in H 1.5 in L