Topic Consolidation: Plane Geometry

Midpoint Theorem

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as the third side.

Intercept Theorem

If a line is parallel to one side of a triangle, it divides the other two sides proportionally.

Alternate Segment Theorem

An angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

The alternate segment theorem states that the red angles are equal to each other and the green angles are equal to each other.

Intersecting Chords Theorem

The Intersecting Chords theorem states that when two chords intersect, no matter where, A*B = C*D.

Tangent-Secant Theorem

DC*CA = DB*DB

If a secant segment and tangent segment are drawn to a circle from the same external point, the product of the length of the secant segment and its external part equals the square of the length of the tangent segment.