7 – Similarity

Skills to Master

  • G.SRT.1a – A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
  • G.SRT.1b – The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
  • G.SRT.2 – Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar.
    • Explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
    • Given a pair of triangles, make a statement about their similarity (similar, not similar, not enough information to prove similarity) and prove your case.
  • G.SRT.4 – Prove theorems about triangles.
    • A line parallel to one side of a triangle divides the other two proportionally.
    • Prove the Pythagorean Theorem using triangle similarity.
  • G.SRT.5 – Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
    • Practice applications of similarity to solve for unknown values or parts.
  • G.SRT.3 – Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
  • G.SRT.5 – Use the properties of similarity transformations to establish the Side-Side-Side (SSS) and Side-Angle-Side (SAS) criterion for two triangles to be similar.

Video Tutorials

Video # 1 – Proportions (Equal Ratios)

#proportional #proportion #ratio

Video # 2 – Scale Factor

#scale #scalefactor #proportionalsides #proportion #triangle #similarity

Video # 3 – Angle Angle Similarity (Defined)

#angleangle #aa #similarity #similar #triangles

Video # 4 – Angle Angle Similarity (Example)

#angleangle #similartriangles #similarity #triangles

Video # 5 – Side Angle Side Similarity (Defined)

#sideangleside #sas #similartriangles #similar #triangles

Video # 6 – Side Angle Side Similarity (Example)

#sas #sideangleside #similar #triangles

Video # 7 – Side Side Side Similarity (Defined)

#sss #ssssimilarity #sidesideside #triangles #similarity

Video # 8 – Side Side Side Similarity (Example)

#sss #ssssimilarity #sidesideside #triangles #similarity

Video # 9 – Determining if Triangles are Similar (Ex 1)

#similar #triangles #similarity #sas #reflexive

Video # 10 – Determining Triangle Similarity (Ex 2)

#similar #triangles #similarity #sas #sss #vertical #reflexive

Video # 11 – Determining Triangle Similarity (Ex 3)

#similar #triangles #similarity #aa #trianglesum

Video # 12 – Angle Bisector Proportional Side Theorem

#anglebisector #proportional #side #theorem #similarity

Video # 13 – Triangle Proportionality Theorem

#triangle #proportionality #theorem

Video # 14 – Right Triangle / Altitude Similarity Theorem (Lesson & Simple Examples)

#Right #Triangle #Altitude #Similarity #Theorem #geometricmean #means #extremes #similar

Video # 15 – Right Triangle / Altitude Similarity Theorem (Multi-Step Examples)

#Right #Triangle #Altitude #Similarity #Theorem #geometricmean #means #extremes #similar #pythagorean #radical

Notes

IM2-7.1a-Notes-Key-by-Hand-Similarity-Transformation-Review

IM2-7.2a-Notes-Key-by-Hand-Similarity-Intro-to-Similar-Triangles

IM2-7.2b-Notes-Key-by-Hand-Similarity-Scale-Factor

Links