Geometry Semester 2 Final Study Guide – Flashcards
104 test answers
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Kite
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A quadrilateral with two pairs of congruent sides and no congruent opposite sides; diagonals are perpendicular; symmetry; longer diagonal line of symmetry.
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Trapezoid
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A quadrilateral with exactly one pairs of parallel sides.
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Isosceles Trapezoid
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A trapezoid in which the nonparallel opposite sides (leg) are congruent; base angles are congruent; diagonals are congruent.
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Consecutive Angles
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Angels that are opposite of each other.
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Base Angles of Trapezoid
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The two angles that share a base.
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Mid-segment of a Trapezoid
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Line segment connecting the midpoints of the legs; runs parallel to the bases of the trapezoid; its length is the average of the base length.
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Properties of Parallelograms/Prove a Quadrilateral is Parallelogram
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Both pairs of opposite sides are parallel; both pairs of opposite sides are congruent; both pairs of opposite angles are congruent; consecutive angles are supplementary; the diagonals bisect each other; show that one pair of sides are simultaneously congruent and parallel.
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Theorem 6-4
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If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on very transversal/
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Properties of a Rhombus
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All the properties of a parallelogram; the diagonals bisect the vertex angles; the diagonals are perpendicular.
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Properties of a Rectangle
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All the properties of a parallelogram; the diagonals are congruent(distance formula).
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Properties of a Square
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All the properties of a parallelogram, rhombus and rectangle.
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Circle
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The set of all the points equidistant from the given point.
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Radius
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Segment from center to vertex.
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Diameter
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A segment that contains the center of the circle and has both endpoints on the circle.
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Central Angle
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Formed by two consecutive radii with the center as its vertex; 360/n (n= number of sides).
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Semicircle
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Arc whose measure equals 180 degrees; named using three letters.
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Minor Arc
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Arc who measure is between 0 and 180 degrees; named using three letters.
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Major Arc
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Arc whose measure i s between 180 and 360 degrees; named using three letters.
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Adjacent Arc
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Arcs in the same circle with any one point in common.
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Circumference
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Distance around a circle; C=(pi)(d) or 2(pi)(r).
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Arc Length
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Part of the circle's circumference.
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Congruent Arc
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Arcs that have the same measure and length.
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Sector of a Circle
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Fraction of a circle, formed by two radii and arc; named same as central angle.
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Segment of a Circle
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Formed by arc and segment connecting end points.
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Pythagorean Theorem
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(aa)+(bb)=(cc)
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Area of a Rectangle
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A=bh
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Area of a Parallelogram
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A=bh
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Area of a Triangle
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A=1/2bh A= 1/2anSin<C
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Area of a Trapezoid
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A=1/2h(b1 + b2)
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Area of a Rhombus of a Kite
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A= 1/2(d1*d2)
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Area of a Regular Polygon
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A= 1/2ap
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Formula for Arc Length
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length of arc AB= measure of arc AB/360 *2(pi)(r)
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Area of a Circle
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A=(pi)(r2)
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Area of a Sector of a Circle
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measure of arc AB/360 * (pi)(r2)
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Heron's Formula
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Find are if given all sides (SSS); are of a triangle; =the square root of(s(s-a)(s-b)(s-c) where s= a+b+c/2.
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45-45-90 Triangle
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short leg=x; long leg=x hypotenuse=xroot2
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30-60-90 Triangle
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short leg=x: long leg= xroot3; hypotenuse=2x
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Ratio
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a comparison of two quantities measured in the same unit; will always be reduced to lowest terms and will have no units.
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Proportions
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a statement that two ratios are equal; have three or more ratios are equal then they can be written as an extended proportion.
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Scale Drawing
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A drawing that is either an enlargement or a reduction of an object.
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Scale Factor
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The amount of enlargement or reduction is referred to as.
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Quadratic Formula
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X= -b + - the square root of b2 -4ac/ 2a
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Similar Polygons
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All corresponding angles must be congruent; all corresponding sides must be proportional.
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Angle-Angle Similarity Postulate
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If two angles of one triangle are congruent to two angles in another triangle, then the triangles are similar.
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Side-Angle-Side Similarity Postulate
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If an angle of one triangle is congruent to one angle in another and the sides including the angles are proportional, then the triangles are similar.
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Side-Side-Side Similarity Theorem
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If three sides of one triangle are proportional to corresponding sides in another triangle, then the triangles are similar.
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Indirect Measurements
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Uses similar triangles and proportions to find distances that would otherwise be difficult to find.
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Geometric Means
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A proportion in which the "means" in the proportion have the same value.
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Theorem 8-3
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The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
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Side-Splitter Theorem
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If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
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Corollary to the Side Slitter Theorem
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If three parallel ones intersect two transversals then the segments intercepted on the transversal are proportional.
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Triangle-Angle-Bisectors Theorem
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If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other sides of the triangle.
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Similarity Ratio (Scale Factor):
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Ratio of corresponding parts of similar figures; comparison of LINEAR elements( lengths).
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SOH-CAH-TOA
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Sine=opposite/hypotenuse; cosine= adjacent/hypotenuse; tangent=opposite/adjacent
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Trig inverse
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Used to find angle measures
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Angle of Elevation
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Is measured upward from the horizontal to line of sight.
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Angle of Depression
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Is measure downward from the horizontal to line of sight.
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Polyhedrons
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3 dimensional figure whose faces are polygons.
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Faces
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Planes
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Edges:
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Lines/segments
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Vertices
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Points (corners)
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Euler's Formula
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F+V=E+2
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Platonic Sides
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Regular polyhedrons. They are regular because all of their faces are congruent regular polygons.
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Tetrahedron
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4 faces
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Hexahedron
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5 faces
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Octahedron
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8 faces
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Dodecahedron
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12 faces
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Icosahedron
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20 faces
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Net
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2 dimensional pattern that folds into a 3 dimensional figure.
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Prism
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Polyhedron with 2, congruent, parallel faces and regular faces( lateral faces); named by the shape of its base.
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Lateral Area
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Area of all lateral faces.
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Surface Area
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Area of all faces( lateral faces plus both bases).
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Right Cylinder
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A cylinder where the height is a side of the cylinder.
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Oblique Cylinder
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A cylinder where the height is outside of the cylinder.
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Lateral Area of a Cylinder
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2(pi)(r)(h)
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Surface Area of a Cylinder
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2(pi)(r)(h) + 2(pi)(r2)
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Volume of a Cylinder
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(pi)(r2)(h)
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Slant Height
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The height that comes off of the base of a pyramid of cone that goes to the vertex.
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Lateral Area of a Pyramid
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n(1/2sl)
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Surface Area of a Pyramid
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n(1/2sl) + s2
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Volume of a Pyramid
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1/3Bh
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Lateral Area of Cone
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(pi)(r)(l)
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Surface Area of a Cone
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(pi)(r)(l) + (pi)(r2)
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Volume of a Cone
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1/3/(pi)(r2)(h)
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Sphere
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The set of points in space equidistant from a given point(the center).
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Surface Area of a Sphere
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4(pi)(r2)
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Volume of a Sphere
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4(pi)(r3)/3
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Tangent Line
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Line that intersects a circle in exactly one point (called the point of tangency)
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Theorem 11-1
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A tangent line is perpendicular to a radius to the point of tangency
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Theorem 11-3
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Two segments tangent to a circle from a point outside the circle are congruent.In addition to the two segments being congruent, line AB is congruent to line CB.
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Chord
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A segment whose end points are on a circle.
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Theorem 11-4
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Within a circle or congruent circles, congruent angles have congruent chords; within a circle or congruent circles congruent chords have congruent arcs; within a circle or congruent circles, congruent arcs have congruent central angles.
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Theorem 11-5
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Within a circle or congruent circles, chord equidistant from the center are congruent and congruent chords are equidistant from the center.
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Theorem 11-6
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In a circle, a diameter or radius is perpendicular to a chord if and only if it bisects the chord and its arc.
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Inscribed Angles
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An angle in a circle whose vertex is on the circle and its sides are chords of the circle. An inscribed angle is never a central angle.
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Theorem 11-9
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The measure of a inscribed angle is half the measure of the intercepted arc. Two inscribed angles that intercept tc are congruent. An angle inscribed in a semicircle is a right angle. The opposite angle of a quadrilateral inscribed a circle are supplementary.
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Theorem 11-10
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The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
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Inscribed and Circumscribed
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A circle is inscribed in a quadrilateral and a quadrilateral is circumscribed around the circle.
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Secant Lines
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A line that intersects a circle at exactly two points.
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Theorem 11-11
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The measure of a vertical angle formed by two secant line sis half of the sum of the two intercepted arcs; the measure of the angle formed by two secant lines is half of the difference of the intercepted arcs; the measure of the angle formed by a secant line and a tangent line is half of the difference of the intercepted arcs; the measure of the angle formed by two tangent lines is half of the difference of the major arc and the minor arc. M
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