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

No Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.