1 1/23/15 Unit 7 Congruency and Similarity (AA, SSS, SAS) Proving Triangles Similar.

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1 1/23/15 Unit 7 Congruency and Similarity (AA, SSS, SAS) Proving Triangles Similar

2 AA Similarity (Angle-Angle) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar….or the third pair of angles are congruent. Conclusion: andGiven:

3 SSS Similarity (Side-Side-Side) If the measures of the corresponding sides of two triangles are in the same ratio, then the triangles are similar. Given: Conclusion:

4 SAS Similarity (Side-Angle-Side) If the measures of two sides of a triangle are in the same ratio to the measures of two corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar. Given: Conclusion:

5 Similarity is reflexive, symmetric, and transitive. 1. Mark the Given. 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 Given Alternate Interior <s AA Similarity Alternate Interior <s AA

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 Given Division Property SSS Similarity Substitution SSS 1. IJ = 3LN ; JK = 3NP ; IK = 3LP

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 4: List the Parts in the order of the method with reasons Next Slide…………. Step 5: Is there more? SAS Step 2: Mark the reflexive angles

9 StatementsReasons 1. G is the Midpoint of H is the Midpoint of Given 2. EG = DG and EH = HFDef. of Midpoint 3. ED = EG + GD and EF = EH + HFSegment Addition Post. 4. ED = 2 EG and EF = 2 EHSubstitution Division Property Substitution Reflexive Property SAS Postulate