Chapter 6.3-6.4 Theorems Flashcards
Chord ⊥ Bisector ==> Center Th.
The ⊥ bisector of a chord contains the center of the ⊙.
≅ Tangent Th.
If 2 segments from the same exterior point are tangent to a ⊙, then they are ≅.
Chord Product Th.
If 2 chords intersect inside a ⊙, then the product of the lengths of the segments (parts) of 1 chord is = to the product of the lengths of the segments of the other.
Secant Segment Product Th.
If 2 secant segments are drawn to a ⊙ from an external point, then the products of the lengths of each secant with its external segment are =.
Secant Tangent Product Th.
If a tangent segment and a secant segment are drawn to a ⊙ from an external point, then the square of the lengths of the tangent is = to the product of the lengths of the secant with the length of its external segment.
Central ∠ Inequality Th.
In a ⊙ or ≅ ⊙s containing 2 ≠ central ∠s, the larger angle corresponds to the larger intercepted arc.
Conv. Central ∠ Inequality Th.
In a ⊙ or ≅ ⊙s containing 2 ≠ arcs, the larger arc corresponds to the larger central ∠.
Chord Center Inequality Th.
In a ⊙ or ≅ ⊙s containing 2 ≠ chords, …
• the shorter chord is at the greater distance from the center of the circle.
• the chord nearer the center of the circle has the greater length
Chord Arc Inequality Th.
In a ⊙ or ≅ ⊙s containing 2 ≠ chords, the longer chord corresponds to the greater minor arc.
Conv. Chord Arc Inequality Th.
In a ⊙ or ≅ ⊙s containing 2 ≠ minor arcs, the greater minor arc corresponds to the longer of the chords related to these arcs.
⊥ Bisector Th.
If a point lies on the ⊥ bisector of a segment, then the point is equidistant from the endpoints of the segment.
Conv. ⊥ Bisector Th.
If a point is equidistant from the endpoints of a segment, then it lies on the ⊥ bisector of the segment.
∠ Bisector Th.
If a point lies on the bisector of an ∠, then the point is equidistant from the sides of the ∠.
Conv. ∠ Bisector Th.
If a point is equidistant from the sides of an ∠, then the point lies on the bisector of the angle.
