Proving Triangles Similar

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Proving Triangles Congruent

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Presentation transcript:

Proving Triangles Similar Lesson 5-3 Proving Triangles Similar (AA, SSS, SAS) Lesson 5-3: Proving Triangles Similar

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

SSS Similarity (Side-Side-Side) If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. 5 11 22 8 16 10 Given: Conclusion: Lesson 5-3: Proving Triangles Similar

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. 5 11 22 10 Given: Conclusion: Lesson 5-3: Proving Triangles Similar

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

Lesson 5-3: Proving Triangles Similar Given: DE║GF Prove: DEC ~ FGC Problem #1 Step 1: Mark the given … and what it implies Step 2: Mark the vertical angles AA 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 C D E G F Given Alternate Interior <s Alternate Interior <s AA Similarity Lesson 5-3: Proving Triangles Similar

Lesson 5-3: Proving Triangles Similar Problem #2 ~ Step 1: Mark the given … and what it implies SSS 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? Statements Reasons 1. IJ = 3LN ; JK = 3NP ; IK = 3LP Given Division Property Substitution SSS Similarity Lesson 5-3: Proving Triangles Similar

Lesson 5-3: Proving Triangles Similar Given: ABCD is a rectangle. Prove: Problem #3 Statements Reasons Lesson 5-3: Proving Triangles Similar

Lesson 5-3: Proving Triangles Similar Problem #4 ~ Step 1: Mark the given … and what it implies Step 2: Mark the reflexive angles SAS 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? Lesson 5-3: Proving Triangles Similar

Lesson 5-3: Proving Triangles Similar Statements Reasons G is the Midpoint of H is the Midpoint of Given 2. EG = DG and EH = HF Def. of Midpoint 3. ED = EG + GD and EF = EH + HF Segment Addition Post. 4. ED = 2 EG and EF = 2 EH Substitution Division Property Reflexive Property SAS Postulate Lesson 5-3: Proving Triangles Similar