Lesson 5-3: Proving Triangles Similar 1 Lesson 6-3 Similar Triangles The following must occur for triangles to be similar, but there are other short cuts.

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Presentation transcript:

Lesson 5-3: Proving Triangles Similar 1 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 2 AA Similarity (Angle-Angle) If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar. Conclusion: andGiven:

Lesson 5-3: Proving Triangles Similar 3 SSS Similarity (Side-Side-Side) If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. Given: Conclusion:

Lesson 5-3: Proving Triangles Similar 4 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. Given: Conclusion:

Lesson 5-3: Proving Triangles Similar 5 Similarity is reflexive, symmetric, and transitive. 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. Steps for proving triangles similar: Proving Triangles Similar

Lesson 5-3: Proving Triangles Similar 6 Problem #1 C D E G F 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? StatementsReasons || ▲▲

Lesson 5-3: Proving Triangles Similar 7 Problem #2 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 Step 5: Is there more? StatementsReasons ▲ ▲

Lesson 5-3: Proving Triangles Similar 8 Problem #3 Step 1: Mark the given … and what it implies Step 3: Choose a method: (AA,SSS,SAS) Step 2: Mark the reflexive angles

Lesson 5-3: Proving Triangles Similar 9 Determine whether each pair of triangles is similar. Justify your answer (AA, SSS, or SAS Similarity) A B C D E F A BC ED A B C D E F A BC

Lesson 5-3: Proving Triangles Similar 10 Identify the similar triangles, and find x and the measure of the indicated sides. x x - 8 A B C D E AB and BC

Lesson 5-3: Proving Triangles Similar 11 Identify the similar triangles, and find x and the measure of the indicated sides. 8 5 x A E B D C AB and AC

Lesson 5-3: Proving Triangles Similar 12 If PR || KL, KN = 9, LN = 16, PM = 2(KP), find KP, KM, MR, ML, MN, and PR. LN K R Q P M