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Lesson 6-3 Similar Triangles The following must occur for triangles to be similar, but there are other short cuts to prove if triangles are similar (AA, SSS, SAS) : 1) The angles must be congruent 2) Sides must be proportional Lesson 5-3: Proving Triangles Similar 1 AA Similarity (Angle-Angle) If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar. E B A C Given: D F and Conclusion: Lesson 5-3: Proving Triangles Similar 2 SSS Similarity (Side-Side-Side) If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. E B 5 A 10 8 11 C D 16 22 F Given: Conclusion: Lesson 5-3: Proving Triangles Similar 3 SAS Similarity (Side-Angle-Side) If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar. E B 5 A 10 11 C D 22 F Given: Conclusion: Lesson 5-3: Proving Triangles Similar 4 Proving Triangles Similar Similarity is reflexive, symmetric, and transitive. Steps for proving triangles similar: 1. Mark the Given . . . and what it implies. 2. Mark … Shared Angles or Vertical Angles 3. Choose a Method. (AA, SSS , SAS) Think about what you need for the chosen method and be sure to include those parts in the proof. Lesson 5-3: Proving Triangles Similar 5 Given : DE || FG Problem #1 Pr ove : ▲ DEC ▲FGC Step 1: Mark the given … and what it implies Step 2: Mark the vertical angles Step 3: Choose a method: (AA,SSS,SAS) Step 4: List the Parts in the order of the method with reasons Step 5: Is there more? Statements Reasons G D C E F Lesson 5-3: Proving Triangles Similar 6 Problem Given : IJ 3LN JK 3NP #2 Pr ove : ▲ IJK ▲LNP IK 3LP Step 1: Mark the given … and what it implies Step 2: Choose a method: (AA,SSS,SAS) Step 4: List the Parts in the order of the method with reasons Statements Reasons Step 5: Is there more? J K N I IJ JK IK 2. =3, =3, =3 LN NP LP P IJ JK IK 3. = = LN NP LP L Lesson 5-3: Proving Triangles Similar 7 Given : G is the midpo int of ED Problem #3 H is the midpo int of EF Pr ove : EGH EDF Step 1: Mark the given … and what it implies Step 2: Mark the reflexive angles Step 3: Choose a method: (AA,SSS,SAS) E G H D Lesson 5-3: Proving Triangles Similar F 8 Determine whether each pair of triangles is similar. Justify your answer (AA, SSS, or SAS Similarity). E 4.5 B 4 3 A 5 6 D 7.5 C A F B C D E E A 12 B 6 A D 8 C 16 F 20 B 18 36 Lesson 5-3: Proving Triangles Similar C 24 9 Identify the similar triangles, and find x and the measure of the indicated sides. AB and BC A x+3 B E 5 3 2x - 8 D C Lesson 5-3: Proving Triangles Similar 10 Identify the similar triangles, and find x and the measure of the indicated sides. A AB and AC x+2 8 E 5 D B 6 C Lesson 5-3: Proving Triangles Similar 11 If PR || KL, KN = 9, LN = 16, PM = 2(KP), find KP, KM, MR, ML, MN, and PR. L N R Q K P M Lesson 5-3: Proving Triangles Similar 12