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

- use markings and notations to identify congruent corresponding angles and proportional corresponding sides of triangles
**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

- construct and make conjectures about the relationship that forms by creating the
**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

- construct a

Develop conceptual understanding:

scale factor, midsegment, medial or midpoint triangleSupporting 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