Evidence of Understanding

**construct medians and explain why****they intersect at the***centroid*- make conjectures about the relationship of the segment lengths that result from constructing 3 medians and prove that the segment lengths are in a ratio of 2:1
- make conjectures about the relationship of the areas of each triangle formed and prove they are the same (connection to center of mass)
- find missing values in a triangle that involve the median
- use tools and counterexamples to prove statements about triangles

**apply perpendicular bisectors to identify the***circumcenter*- construct
**perpendicular bisectors**and apply transformations to justify the location of the**circumcenter** - make conjectures and justify why if two perpendicular bisectors intersect each other, then the third perpendicular bisector would intersect at the same point
- show the point of intersection is equidistant to the vertices of each side of the triangle it is perpendicularly bisecting

- show the point of intersection is equidistant to the vertices of each side of the triangle it is perpendicularly bisecting

- construct
**construct altitudes and use them to determine the***orthocenter*- prove the triangles formed by constructing the
**altitude**are similar - analyze the relationship between the
**orthocenter**of a medial triangle and the circumcenter of its larger triangle and prove why they are the same point- explain how the perpendicular bisectors of the larger triangle are the same as the altitudes of the medial triangle

- make conjectures, using tools, about the location of the orthocenter in relationship to the triangle (right, acute, obtuse) and how the angle measures impact the location
- explain why the orthocenter of a right triangle always lies at the vertex of the triangle’s right angle

- prove the triangles formed by constructing the

Develop conceptual understanding:

median, centroid, perpendicular bisectors, circumcenter, altitude, orthocenterSupporting terms to communicate:

vertex, midpoint, opposite side, proportional, ratio, scale factor, area, similar, equidistant, right, obtuse, acute, reflection, rotation, dilation, center of dilation, corresponding