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Exploring Triangles and Polygons: Key Concepts and Formulas

Dive into the world of geometry with this detailed guide on segments connecting triangle midpoints, isosceles triangles, centroids, medians, altitudes, and more. Learn about midsegments, regular polygons, and how to find angle measurements efficiently.

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Exploring Triangles and Polygons: Key Concepts and Formulas

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  1. Unit 4 Vocabulary

  2. Midsegment • Segments connecting the midpoints of triangles • Creates 4 congruent triangles within the triangle

  3. Isosceles Triangles • Base side: • Base angles:

  4. Centroid • POC of the medians

  5. Median • Segment connecting the midpoint of a side to the opposite vertex.

  6. Altitude • Segment from a vertex that intersects the opposite side at a right angle. “Height”

  7. Orthocenter • POC of the altitudes

  8. Constructing Altitude (or a perpendicular line through a point) • From the point, make an arc that intersects the line twice. • Now bisect the segment you made on the line. • Draw in the perpendicular line—remember, it should intersect the point and the two “fish tails”.

  9. Midsegments • The midsegment joining the midpoints of two sides are parallel to the 3rd side of the triangle. • They are also half the length of that side.

  10. Regular Polygons • Polygons that are equilateral (all sides are congruent) and equiangular (all angles are congruent)

  11. Finding the measure of one angle. Formula:

  12. Exterior Angles • Interior and exterior angles are supplementary. • I + E = 180 • Formula:

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