Big Idea:

Big Idea 2

Congruent corresponding angles and proportional corresponding sides are used to prove triangles are similar.

1 week

Evidence of Understanding

  • prove triangles are similar and solve problems in geometric figures using congruence and similarity criteria for triangles
    • use markings and notations to identify congruent corresponding angles and proportional corresponding sides of triangles
      • map figures onto one another in the plane and identify corresponding angles and sides
    • use information about triangle similarity and congruence to determine which information is required to prove figures are similar
      • apply transformations to re-draw figures and explain the corresponding relationships between the two diagrams drawn
      • explain the angle where the center of dilation is the vertex using reflexive property
      • apply properties of parallel lines to prove figures are similar
    • find missing values by applying the relationships of sides (scale factor) and angles
       
  • prove characteristics about the midsegment of a triangle
    • construct and make conjectures about the relationship that forms by creating the midsegment
    • prove that the midsegment is parallel to one side of a triangle and divides the other two proportionally
      • prove that midsegments have the same relationship in quadrilaterals
    • use midsegments to prove relationships between figures and find missing measurements
       
  • prove characteristics about the medial triangle (also called the midpoint triangle)
    • construct a medial triangle and make conjectures about the relationships of triangles formed
    • apply properties of parallel lines to prove similarity and congruence relationships between the larger triangle and the other triangles created within it
      • prove the medial triangle (or one of the other three) is similar to the larger triangle
      • prove the medial triangle is congruent to the other 3 triangles created within the larger triangle

Develop conceptual understanding:

scale factor, midsegment, medial or midpoint triangle

Supporting terms to communicate:

proportional, ratio, corresponding, dilation, center of dilation, rotation, reflection, translation, vertex, similarity, congruence, AA, SAS, ASA, AAS, SSS, midpoint, bisect, parallel, partition
Core Resource
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