Similarity Theorems

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Similarity Theorems. Similarity in Triangles. Angle-Angle Similarity Postulate (AA~) - If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. W. V. S. 45 . 45 . WRS  BVS because of the AA~ Postulate. R. B. - PowerPoint PPT Presentation

Text of Similarity Theorems

  • SIMILARITY THEOREMS

  • Similarity in TrianglesAngle-Angle Similarity Postulate (AA~)- If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.WRS BVS because of the AA~ Postulate.

  • Similarity in TrianglesSide-Angle-Side Similarity Postulate (SAS~)- If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the angles are proportional, then the triangles are similar.TEA CUP because of the SAS~ Postulate.The scale factor is 4:3.

  • Similarity in TrianglesSide-Side-Side Similarity Postulate (SSS~)- If the corresponding sides of two triangles are proportional, then the triangles are similar.ABC QRS because of the SSS~ Postulate.The scale factor is 1:5.

  • Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used.Yes, FGH KJH because of the AA~ Postulate

  • Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used.

  • Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used.AXYBC20252530

  • Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used.Yes, APJ ABC because of the SSS~ Postulate.

  • Explain why these triangles are similar. Then find the value of x.4.5xThese 2 triangles are similar because of the AA~ Postulate. x=7.5

  • Explain why these triangles are similar. Then find the value of x.These 2 triangles are similar because of the AA~ Postulate. x=2.557011033x

  • Explain why these triangles are similar. Then find the value of x.221424x

  • Explain why these triangles are similar. Then find the value of x.These 2 triangles are similar because of the AA~ Postulate. x= 12x629

  • Explain why these triangles are similar. Then find the value of x.These 2 triangles are similar because of the AA~ Postulate. x=8154x5

  • Explain why these triangles are similar. Then find the value of x.These 2 triangles are similar because of the AA~ Postulate. x= 15187.512x

  • Please complete the Ways to Prove Triangles Similar Worksheet.

  • Side Splitter Theorem - If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.Similarity in Triangles

  • TheoremIf three parallel lines intersect two transversals, then the segments intercepted are proportional.

  • TheoremTriangle Angle Bisector Theorem -If a ray bisects an angle of a triangle, then it divides the opposite side on the triangle into two segments that are proportional to the other two sides of the triangle.

  • Please complete pg. 449: 1-24, 31-33.