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Chapter 10 Axioms
List of chapter 10 axioms for Geometry for Enjoyment and Challenge
| Question | Answer |
|---|---|
| A ___ is the set of all points in a plane that are a given distance from a given point in the plane. | Circle |
| The point that names the circle is the ___ of the circle. | Center |
| The distance from the center of a circle to the circle is the ___. | Radius |
| A ___ is the chord that passes through the center of the circle. | Diameter |
| A ___ is equal in length to two radii. | Diameter |
| All radii of the same circle are ___. | Congruent |
| The circumference of a circle = ___. | d(pi) |
| The area of a circle = ___. | r-squared(pi) |
| The length of an arc = ___. | %C - The % is the measure of the arc divided by 360 |
| The area of a sector = ___. | %A - The % is the measure of the arc divided by 360 |
| Two or more coplanar circles with the same center are called ___ circles. | Concentric |
| A point is ___ ( in the ___ of ) a circle if its distance from the center is less than the radius. | Inside, Interior |
| A point is ___ ( in the ___ of ) a circle if its distance from the center is greater than the radius. | Outside, Exterior |
| A point is ___ a circle if its distance from the center is equal to the radius. | Equidistant |
| A ___ of a circle is a segment joining any 2 points on the circle. | Chord |
| A ___ of a circle is a chord that passes through the center of the circle. | Diameter |
| The distance from the center of a circle to a chord is the measure of the ___ segment from the center to the chord. | Perpendicular |
| If a radius is perpendicular to a chord, then ___. | It Bisects the Chord |
| If a radius of a circle bisects a chord that is not a diameter, then ___. | It is Perpendicular to that Chord. |
| The ___ of a chord passes through the center of the circle. | Perpendicular Bisector |
| If two chords of a circle are equidistant from the center of a circle, then ___. | The Chords are Congruent |
| If two chords of a circle are congruent, then ___. | The Chords are Equidistant |
| An ___ consists of 2 points on a circle and all points on the circle needed to connect the points by a single path. | Arc |
| The ___ of an arc is is the center of the circle of which the arc is a part. The unit is ___. | Measure, Degrees |
| A ___ is an angle whose vertex is on the center of a circle. | Central Angle |
| A ___ is an arc whose points are on or between the sides of a central angle. | Minor Arc |
| A ___ is an arc whose points are on or outside of a central angle. | Major Arc |
| A ___ is an arc whose endpoints are the endpoints of a diameter. | Semicircle |
| The measure of a minor arc or a semicircle is ___ the measure of the central angle that intercepts the arc. | The Same As |
| The measure of a major arc is 360 minus the measure of ___ with the same endpoints. | The Minor Arc |
| Two arcs are ___ whenever they have the same measure and are parts of the same circle or congruent circles. | Congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent, then ___. | Their Intercepted Arcs are Congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent, then ___. | The Corresponding Central Angles are Congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent, then ___. | The Corresponding Chords are Congruent |
| If 2 chords of a circle (or of congruent circles) are congruent, then___. | The Corresponding Central Angles are Congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent, then ___. | The Corresponding Chords are Congruent |
| If 2 chords of a circle (or of congruent circles) are congruent, then ___. | The Corresponding Arcs are Congruent |
| A ___ is a line that intersects a circle at exactly 2 points. (Every ___ contains a chord of the circle.) | Secant |
| A ___ is a line that intersects a circle at exactly ___ point. This point is called the ___ or point of contact. | Tangent, 1, Point of Tangency |
| A tangent line is ___ to the radius drawn to the point of contact. | Perpendicular |
| If a line is perpendicular to a radius at its outer endpoint, then ___. | It is Tangent to the Circle |
| A ___ is the part of a tangent line between the points of contact and a point outside the circle. | Tangent Segment |
| A ___ is the part of a secant line that joins a point outside the circle to the farther intersection point of the secant and the circle. | Secant Segment |
| The ___ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point. | External Part |
| If 2 tangent segments are drawn to a circle form an external point, then ___. | Those Segments are Congruent |
| ___ are circles that intersect each other at exactly one point. | Tangent Circles |
| Two circles are ___ if each of the tangent circles lies outside the other. | Externally Tangent |
| Two circles are ___ if one of the tangent circles lies inside the other. | Internally Tangent |
| A ___ is a line tangent to two circles (not necessarily at the same point). Such a tangent is a ___ if it lies between the circles (intersects the segment joining the centers) or a ___ if it is not between the circles. | Common Tangent, Common Internal Tangent, Common External Tangent |
| An ___ is an angle whose vertex is on a circle and whose sides are determined by two chords. | Inscribed Angle |
| A ___ angle is an angle whose vertex is on a circle and whose sides are determined by a tangent and a chord that intersect at the tangent's point of contact. | Tangent-Chord |
| The measure of an inscribed angle or a tangent-chord angle (vertex on a circle) is ___. | One-Half the Measure of its Intercepted Arc |
| A ___ angle is an angle formed by 2 chords that intersect inside a circle but not at the center. | Chord-Chord |
| The measure of a chord-chord angle is ___. | One-Half the Sum of the Measures of the Arcs Intercepted by the Chord-Chord Angle and its Vertical Angle |
| A ___ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 secants. | Secant-Secant |
| A ___ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent. | Secant-Tangent |
| A ___ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. | Tangent-Tangent |
| The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside a circle) is ___. | One-Half the Difference of the Measures of the Intercepted Arcs |
| If 2 inscribed or tangent-chord angles intercept the same arc, then ___. | They are Congruent |
| If the vertex of an angle is ___ the circle, then to find the measure of the angle, use ___. | In, (Arc+Arc)/2 |
| If the vertex of an angle is ___ the circle, then to find the measure of the angle, use ___. | On, (Arc)/2 |
| If the vertex of an angle is ___ the circle, then to find the measure of the angle, use ___. | Out, (Arc-Arc)/2 |
| If 2 inscribed or tangent-chord angles intercept congruent arcs, then ___. | They are Congruent |
| An angle inscribed ina semi-circle is a ___. | Right Angle |
| The sum of the measures of a tangent-tangent angle and its minor arc is ___. | 180 |
| A polygon is ___ a circle if all of its vertices lie on the circle. | Inscribed In |
| A polygon is ___ a circle if each or its sides is tangent to the circle. | Circumscribed About |
| The center of a circle circumscribed about a polygon is the ___ of the polygon. | Circumcenter |
| The center of a circle inscribed in a polygon is the ___ of the polygon. | Incenter |
| If a quadrilateral is inscribed by a circle, ___. | Its Opposite Angles are Supplementary |
| If a parallelogram is inscribed in a circle, ___. | It Must Be a Rectangle |
| If 2 chords of a circle intersect inside the circle, then ___. | The Product of the Measures of the Segments of One Chord is Equal to the Product of the Measures of the Segments of the Other Chord |
| If a tangent segment and a secant segment are drawn from an external point to a circle, then ___. | The Square of the Measure of the Tangent Segment is Equal to the Product of the Measures of the Entire Secant Segment and its External Part |
| If 2 secant segments are drawn from an external point to a circle, then ___. | The Product of the Measure of One Secant Segment and its External Part is Equal to the Product of the Measures of the Other Secant Segment and its External Part |
| The ___ of a circle is its perimeter. | Circumference |
| The formula for the circumference of a circle is ___. | C=(pi)d |
| The length of an arc is equal to ___. | The Circumference of its Circle times the Fractional Part of the Circle Determined by the Arc Length of PQ=(mPQ/360)(pi)d Where d is the Diameter and PQ is Measured in Degrees |
Created by:
Ethan_R
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