Term
| Chord Central Angles Theorem |
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Definition
| If 2 chords in a circle are congruent, then they determine 2 central angles that are congruent |
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Term
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Definition
| If 2 Chords in a circle are congruent, then their arcs are congruent |
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Term
| Perpendicular to a Chord Theorem |
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Definition
| The perpendicular from the center of a circle to a chord is the bisector of that chord |
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Term
| Chord Distance to Center Theorem |
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Definition
| Two congruent chords in a circle are equidistant from the center of a circle |
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Term
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Definition
| A tangent to a circle is perpendicular to the radius drawn to the point of tangency |
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Term
| Tangent Segments Conjecture |
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Definition
| Tangent segments to a circle from a point outside the circle are congruent |
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Term
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Definition
| The measure of an angle inscribed in a circle is half the measure of its central angle |
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Term
| Inscribed Angles Intercepting Arcs Theorem |
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Definition
| Inscribed Angles that intercept the same arc are congruent |
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Term
| Angles Inscribed in a Semicircle Theorem |
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Definition
| Angles inscribed in a semicircle are right |
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Term
| Cyclic Quadrilateral Theorem |
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Definition
| The opposite angles of cyclic quadrilateral are supplementary |
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Term
| Parallel Lines Intercepted Arcs Theorem |
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Definition
| Parallel lines intercept congruent arcs in a circle |
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Term
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Definition
| The circumference of a circle is d(pi) or 2r(pi) |
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Term
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Definition
| The length of an arc equals the measure of its angle/360 x 2(pi)r |
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Term
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Definition
| The area of a rectangle is found by the formula A=bxh, where A is the area, b is the length of the base and h is the height |
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Term
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Definition
| The area of a parallelogram is found by the formula A=bxh, where A is the area, b is the length of the base, and h is the height |
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Term
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Definition
| The area of a triangle is found by the formula .5xbxh=A, where A is the area, b is the base, and h is the height |
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Term
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Definition
| The area of a trapezoid is found by the formula .5(b1+b2) x h |
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Term
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Definition
| The area of a kite is found by the formula .5xd1xd2 |
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Term
| Area of a Regular Polygon |
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Definition
| The area of a regular polygon is found by A=.5nas or A=.5aP |
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Term
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Definition
| The area of a circle is found by the formula A=(pi)r squared |
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Term
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Definition
| In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the hypotenuse |
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Term
| Converse of the Pythagorean Theorem |
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Definition
| If the sum of the squares of the legs equals the square of the hypotenuse, then the triangle is right |
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Term
| Isosceles Right Triangle Theorem (45-45-90) |
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Definition
| In an isosceles right triangle if the legs have length of l, then the hypotenuse has length lxsquare root of 2 |
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Term
| 30-60-90 Triangle Theorem |
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Definition
| In a 30-60-90 degree triangle, if the shorter leg has length of a, then the longer leg has length of ax(square root of 3), and the hypotenuse will have length 2a |
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Term
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Definition
| The distance between points A(x1,y1) and B(x2, y2) is given by (AB)(squared)= (x2-x1)(squared) + (y2-y1)(squared) |
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Term
| Area of a Right or Oblique Prism and Cylinder |
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Definition
| If B= the area of the base, and h equals the height, then V=Bh |
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Term
| Area of a Right or Oblique Pyramid and Cone |
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Definition
| If B equals the area of the base, and h equals the height, then V=(1/3)Bh |
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Term
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Definition
| The volume of a sphere with radius r is given by the formula 4/3(pi)r(squared) |
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Term
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Definition
| The volume of a sphere with radius r is given by the formula 4(pi)r(squared) |
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Term
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Definition
| If 2 angles of a triangle are congruent to 2 angles of another triangle, then the triangles are similar |
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Term
| SSS Similarity Conjecture |
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Definition
| If three sides of one triangle are proportional to three sides of another triangle, then the two triangles are similar |
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Term
| SAS Similarity Conjecture |
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Definition
| If two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar |
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Term
| Proportional Parts Conjecture |
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Definition
| If two triangles are similar, then the lengths of the corresponding altitudes, medians, and angle bisectors are proportional to the lengths of the corresponding sides |
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Term
| Angle Bisector/Opposite Side Conjecture |
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Definition
| A bisector of an angle in a triangle divides the opposite sides into two segments whose lengths are the same ratio as the lengths of the two sides forming the angle |
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Term
| Proportional Areas Conjecture |
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Definition
| If two corresponding side lengths of 2 similar polygons or the radii of 2 circles compare in the ratio m/n, then their areas compare in the ratio m(squared)/n(squared) |
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Term
| Proportional Volumes Conjecture |
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Definition
| If corresponding side lengths of two similar polygons or the radii of two circles compare in the ration m/n, then their volumes compare in the ratio m(cubed)/n(cubed) |
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Term
| Parallel/Proportionality Conjecture |
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Definition
| If a line parallel to one side of a triangle passes through the other two sides, then it divides the other two sides proportionally. Conversely, if a line cuts 2 sides of a triangle proportionally, then it is parallel to the third side. |
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Term
| Right Triangle Similarity Conjecture |
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Definition
| The altitude to the hypotenuse of a right triangle divides the triangle into two right triangles that are similar to each other and the original right triangle |
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Term
| Right Triangle Similarity Theorem 1 |
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Definition
| When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse |
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Term
| Right Triangle Similarity Theorem 2 |
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Definition
| When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean of the hypotenuse and its segment that is adjacent to that leg |
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Term
| Intersecting Secants Theorem |
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Definition
| The measure of an angle formed by two secants that intersect outside a circle is equal to one half the difference of the larger intercepted arc subtracted by the smaller intercepted arc |
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Term
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Definition
| The measure of an angle formed at the intersection at the point of tangency of a tangent an a chord is equal to one-half the intercepted arc |
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Term
| Intersecting Chords Theorem |
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Definition
| The measure of an angle formed by the intersection of two chords is equal to one half the sum of the intersecting arcs |
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Term
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Definition
| The measure of an angle formed by an intersecting tangent and secant is equal to one half the difference of the larger intercepted arc and the smaller intercepted arc |
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Term
| Intersecting Tangents Theorem |
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Definition
| The measure of an angle formed by two intersecting tangents is supplementary to the intercepted arc |
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