Thursday, October 29, 2015

Colorful Constructions with Medians and Altitudes

This activity was to demonstrate the medians and altitudes on acute and obtuse triangles. We drew the medians by finding a vertex of the triangle and drawing a line segment from that vertex to the opposite side, thus creating congruent segments. We drew the altitudes on the acute triangles by finding a vertex of the triangle, and then creating a right angle with the line segment drawn. For obtuse triangles, we extended the obtuse angle so that we could draw the altitude. 

Theorems:
  • Median: 
    • If a segment is drawn from the vertex of a triangle and it divides the opposite side into 2 congruent parts, then it is the median.
    • If a line is drawn from the vertex of a triangle and it divides the opposite side into 2 congruent parts, then that point is a midpoint.
    • If a line is drawn from the vertex of a triangle and it divides the opposite side into 2 congruent parts, then it also bisects the angle of the vertex.
  • Altitude: 
    • If a segment is drawn from the vertex of a triangle and it is perpendicular to the opposite side, then it is an altitude.
    • If a segment is drawn from the vertex of a triangle and it is perpendicular to the opposite side, then the angle created at the intersection is a right angle.
    • If a segment is drawn from from the vertex of a triangle and it is perpendicular to the opposite side, then it creates an angle that is 90ยบ at the intersection (right angle)



No comments:

Post a Comment