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Circles Math Quiz
Circles Geometry
| Term | Definition |
|---|---|
| Radius | Any segment with endpoints that are the center and a point on the circle |
| Center | Given point on the circle (names the circle) |
| Diameter | A chord that passes through the center is a diameter of a circle |
| Chord | Any segment with end points that are on a circle |
| Theorem 1: Congruent central angles/chords/arcs | Congruent central angles will have congruent chords, congruent arcs, and congruent chords will have congruent arcs |
| Theorem 2: Congruent chords/equidistant | Congruent chords will be equidistant from the center of the circle |
| Theorem 3: Diameter/perpendicular/bisect | diameter + perpendicular = bisect Diameter + Bisect = perpendicular Perpendicular + bisect = Diameter |
| Tangent to a Circle | A line in the plane of the circle that intersects the circle in exactly one point |
| Point of tangency | The point where a circle and a tangent intersect |
| Tangent theorem 1 | If a line is tangent to a circle, then it is perpendicular to the radius draw to the point of tangency |
| Converse theorem 1 | If a line is perpendicular to the radius of a circle at its endpoint on a circle then the line is tangent to the circle |
| Tangent theorem 2 | If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent |
| Tangent theory 3 | When a polygon is circumscribed about a circle, all of the sides of the polygon are tangent to the circle |
| Circumcenter | Perpendicular bisectors, same distance from corners, can be outside |
| Incenter | Angle bisectors, same distance from edges, always inside the triangle |
| Centroid | Median, Splits median into 2/3 and 1/3, always inside the triangle |
| Orthocenter | Altitude |
| Medians = | Centroid |
| Perpendicular bisectors = | circumcenter |
| Angle bisector = | Incenter |
| Perpendicular bisector | 90 degrees to a line and cuts it in 1/2 (from midpoint) |
| Angle bisector | Cuts an angle in 1/2 |
| Altitude | A perpendicular that crosses the opposite vertex |
| Median | Goes from midpoint to opposite vertex (Splits evenly) |
| Congruence of perpendicular bisectors | The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices PA = PB = PC |
| Corollary 1 | Two inscribed angles that intercept the same arc are congruent |
| Corollary 2 | An angle inscribed in a semicircle is a right angle |
| Corollary 3 | The opposite angles of a quadrilateral inscribed in a circle are supplementary |
| Tangent chord angle | An angle formed by an intersecting tangent and chord has its vertex "on" the circle |
| Tangent chord angle theorem | The tangent chord angle is half of the measure of the intercepted arc Tangent chord = 1/2 (intercepted arc) |
| Central angle | A central angle is an angle formed by two intersecting radii such as its vertex is at the center of the circle |
| Central angle theorem | In a circle, or congruent circles, congruent central angles have congruent arcs |
| Major arc | An arc using a circle measuring more than or equal to 180 degrees |
| Minor arc | An arc measuring less than 180 degrees |
| Semicircle | An arc of a circle measuring 180 degrees |
| Inscribed angle | An inscribed angle is an angle with it's vertex "on" the the circle, formed by two intersecting chords |
| Inscribed angle theorem | The measure of an inscribed angle is half the measure of its intercepted arc |
Created by:
suiter.mayhew
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