Geometry is about finding basic laws of nature through shapes and
lines. And even though you may not realize the significance of
geometry while still in high school, you probably use it every
day. From playing pool to performing gymnastics to planning
football strategy, geometry plays a huge, if somewhat secretive,
role in our daily lives.
To give you a short taste of geometry, here is Euclid's
postulate and theorems of similar triangles (i.e. triangles that
have the same shape, but aren't necessarily the same size).
Similar Triangles
AA Postulate states that if two angles of one triangle are
congruent (the same) as two angles of another, the triangles are
similar (AA stands for Angle Angle).
Theorem 1. If the lengths of the sides of one triangle
are proportional to the lengths of the sides of a second
triangle, the triangles are similar.
Theorem 2. If a line parallel to one side of a triangle
intersects the other two sides, it divides them
proportionally.
Theorem 3. If a line segment connects the midpoints of
two sides of a triangle, it is parallel to the third side and has
a length half the length of the third side.
Theorem 4. If an altitude is drawn to the hypotenuse of
a right triangle, the new triangles formed are similar to each
other and the given triangle.
Theorem 5. The length of the altitude to the hypotenuse
of a right triangle is the geometric mean of the lengths of the
segments into which the altitude separates the hypotenuse.
Theorem 6. If the altitude to the hypotenuse is drawn
in a right triangle, the length of either leg is the geometric
mean of the lengths of the hypotenuse and the segment of the
hypotenuse which is adjacent to that leg.
Don't worry if all this seems overly complicated right
now—with the right grounding in the basics it'll soon make a lot
more sense to you.
Now you try it...
