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10.1-10.5
Geometry axioms for 10.1-10.5
| Term | Definition |
|---|---|
| A ______________ is the set of all points in a plane that are a given distance from a given point in the plane. (p 439, definition | 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 | diameter |
| All radii of the same circle are _____. (p 439, theorem) congruent 439 T19 | congruent |
| The circumference of a circle = _____ | d(pi) |
| The area of a circle = _____ | r2(pi) |
| The length of an arc = _____ | 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. arc/360 times Area |
| Two or more coplanar circles with the same center are called _____________________ circles. (p 439, definition) 439 D | concentric 439 |
| A point is ____________ (in the ____________ of) a circle if its distance from the center is less than the radius. (p 439, definition) 439 D | inside, interior |
| A point is _____________ (in the ____________ of) a circle if its distance from the center is greater than the radius. (p 439, definition) 440 D | Outside exterior 440 D |
| A point is _____a circle if its distance from the center is equal to the radius. (p 440, definition) | Equidistant |
| A _____ of a circle is a segment joining any 2 points on the circle. | chord 440 D |
| A _____ of a circle is a chord that passes through the center of the circle. | diameter 440 D |
| The distance from the center of a circle to a chord is the measure of the __________________ segment from the center to the chord. 441 D | perpendicular |
| If a radius is perpendicular to a chord, then 441 T74 | it bisects the chord |
| If a radius of a circle bisects a chord that is not a diameter, then . | It is perpendicular to the chord 441 T75 |
| The _____ of a chord passes through the center of a circle. 441 T76 | perpendicular bisector |
| If 2 chords of a circle are equidistant from the center of a circle, then ___. | The chords are congruent 446 T77 |
| If 2 chords of a circle are congruent, then ____. | They are equidistant 446 T78 |
| An _____ consists of 2 points on a circle and all points on the circle needed to connect the points by a single path. | arc 450 D |
| The _____of an arc is the center of the circle of which the arc is a part. The unit is _____ | center, degrees |
| A _____ is an angle whose vertex is at the center of a circle. 450 D | central angle |
| A _____is an arc whose points are on or between the sides of a central angle. 451 D | minor arc |
| A _____ is an arch whose points are on or outside of a central angle. 451 D | major arc |
| A _____ is an arc whose endpoints are the endpoints of a diameter. | semicircle 451 D |
| The measure of a minor arc or a semicircle is _____the measure of the central angle that intercepts the arc. 451 D | same |
| The measure of a major arc is 360 minus the measure of _______ _______________ ______ with the same endpoints. 451 D | the minor arc |
| Two arcs are ________________ whenever they have the same measure and are parts of the same circle or congruent circles. 452 D | congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent, then . 453 T79 | their intercepted arcs are congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent, then 453 T80 | the corresponding central angles are congruent |
| If 2 central angles of a circle (or of congruent circles) are congruent, then 453 T81 | the corresponding chords are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent, then . 453 T82 | then the corresponding central angles are congruent |
| If 2 arcs of a circle (or of congruent circles) are congruent, then . 453 T83 | the corresponding chords are congruent |
| If 2 chords of a circle (or of congruent circles) are congruent, then . 453 T84 | the corresponding arcs are congruent |
| in the same circle or in congruent circles then | congruent chords, congruent arcs, and congruent central angles |
| A __________________ is a line that intersects a circle at exactly 2 points. (Every ______________ contains a chord of the circle.) 459 D | secant, secant |
| A ________________ is a line that intersects a circle at exactly _________ point. This point is called the _________________ ____ ________________ or point of contact. 459 D | tangent, one, point of tangency |
| A tangent line is to the radius drawn to the point of contact. 459 P | perpendicular |
| If a line is perpendicular to a radius at its outer endpoint, then . 459 P | 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. 460 D | 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. 460 D | secant segment |
| The ________________________ ____________________________ of a secant segment is the part of a secant line that joins the outside point to the nearer intersection point. 460 D | external part |
| If 2 tangent segments are drawn to a circle from an external point, then . 460 T85 | then those segments are congruent (Two-Tangent Theorem) |
| __________________________ ________________________ are circles that intersect each other at exactly one point. 460 D | Tangent circles |
| Two circles are ________________________ _______________________ if each of the tangent circles lies outside the other. 460 D | externally tangent |
| Two circles are __________________________________ ______________________ if one of the tangent circles lies inside the other. 460 D | 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 | |
| A is a line tangent to two circles . 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 (does not intersect the segment joining the centers). | common tangent, common internal tangent, common externlal tangent |
| An _____________________ ___________________ is an angle whose vertex is on a circle and whose sides are determined by 2 chords. 469 D | 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. 469 D | tangent-chord angle |
| The measure of an inscribed angles or a tangent-chord angle (vertex on a circle) is . 469 T86 | 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. 470 D | chord-chord angle |
| The measure of a chord-chord angle is 470 T87 | 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. 471 D | secant-secant |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent. 471 D | secant-tangent |
| A __________________________ angle is an angle whose vertex is outside a circle and whose sides are determined by 2 tangents. 471 D | tangent-tangent |
| The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside the circle) is . 471 T88 | one-half the difference of the measures of the intercepted arcs |
| If the vertex of the angle is the center of the circle | angle=arc |
| if the vertex of the angle is in the circle | angle=arc+arc/2 |
| if the vertex of the angle is on the circle | angle=arc/2 |
| if the vertex of the angle is out the circle | angle=arc-arc/2 |
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