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Plane Geometry Chapter 4, Section 15-26: Projection and Numerical Properties of Triangles

Plane Geometry Chapter 4: Proportions and Similar Polygons
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Terms to Know:
Section 15-18: Applications
  • The resultant is represented in direction and value by the diagonal of a parallelogram.
Section 19-24: Numerical and Literal Fractions
  • In representing a ratio expressed as a numerical fraction, any two lines may be used which have this ratio.
  • In representing a ratio expressed as a literal fraction, such as a:b, where the numerical value of the ratio is not given, consider the two terms a and b as any two given lines.
Section 25: Projection
  • The projection of a point upon a line is the foot of the perpendicular from the point to the line.
  • The projection of one line upon another is the locus of the projection of all its points.
Section 26: Numerical Properties of Triangles
  • In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
  • In an obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of those sides and the projection of the other side upon it. 
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