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| 73810826 | Geometric Mean | the number (x) such that a/x = x/b, where a,b, and x are positive numbers | 73810826 | |
| 73810827 | Right Triangle Similarity Theorem | The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and the original triangle | 73810827 | |
| 73810828 | Altitudes Theorem | In a right triangle with an altitude to the hypotenuse, each leg is the geometric mean between the lengths of the two segments on the hypotenuse | 73810828 | |
| 73810829 | Legs Theorem | in a right triangle with an altitude to the hypotenuse, each leg is the geometric mean between the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg | 73810829 | |
| 73810830 | Pythagorean Theorem | a²+b²=c² | 73810830 | |
| 73810831 | Proof of the Pythagorean theorem | 1)given, 2) Legs Theorem, 3) cross multiplication, 4) addition, 5) distributive property, 6) segment addition postulate (c=x+y), 7) substitution | 73810831 | |
| 73810832 | Converse of the Pythagorean Theorem | If c²=a²+b² , then it is a right triangle (used to verify whether the triangle is a right triangle) | 73810832 | |
| 73810833 | Pythagorean Inequality Theorem | If a²+b²>c², the triangle is acute. If a²+b²| 73810833 | | |
| 73810834 | 45-45-90 triangle | x, x, x√2 | 73810834 | |
| 73810835 | 30-60-90 triangle | x, x√3, 2x | 73810835 | |
| 73810836 | Sine, Cosine, and Tangent | (NOT FOR HYPOTENUSE (if hypotenuse, use Pythagorean theorem)) sinA=opp. leg length÷hypotenuse length=measure of angle A cosA=adj. leg length (non-hypotenuse)÷hypotenuse length=measure of angle A tanA=opp. leg length÷adjacent (non-hypotenuse) leg length=measure of angle A | 73810836 | |
| 73810837 | Congruent Circles | Circles with congruent radii | 73810837 | |
| 73810838 | Chord | A segment which joins two points on a circle | 73810838 | |
| 73810839 | Diameter | A chord through the center of the circle | 73810839 | |
| 73810840 | Secant | A line which contains a chord of a circle | 73810840 | |
| 73810841 | Tangent | A line in a plane of the circle which intersects the circle in exactly one (1) point | 73810841 | |
| 73810842 | Point of Tangency | The point at which a tangent intersects the circle | 73810842 | |
| 73810843 | Inscribed | A polygon in a circle where all its vertices are on the circle | 73810843 | |
| 73810844 | Circumscribed | A polygon around a circle where all of its sides are tangent to the circle | 73810844 | |
| 73810845 | Concentric Circles | Two circles in the same plane with the same center | 73810845 | |
| 73810846 | Theorem | If a line is perpendicular to a radius of a circle at a point on the circle, then the line is tangent to the circle | 73810846 | |
| 73810847 | Theorem | If a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency. | 73810847 | |
| 73810848 | Theorem | Two tangent segments from a point on the exterior of a circle are congruent. | 73810848 | |
| 73810849 | Corollary (of "Two tangent segments from a point on the exterior of a circle are congruent.") | The line through an external point and the center of a circle bisects the angle formed by the two tangents from an external point. | 73810849 | |
| 73810850 | Common Tangent | A line that is common to two coplanar circles | 73810850 | |
| 73810851 | External Tangent | A line that is common to two coplanar circles, and does not intersect the segment which joins the centers of the circles | 73810851 | |
| 73810852 | Internal Tangent | A line that is common to two coplanar circles and which does intersect the segment joining the centers of the two circles | 73810852 | |
| 73810853 | Arc | Two points and a continuous part of a circle between them | 73810853 | |
| 73810854 | Central Angle | An angle whose vertex IS the center of the circle | 73810854 | |
| 73810855 | Minor Arc | The arc on the interior of the central angle | 73810855 | |
| 73810856 | Major Arc | The arc on the exterior of the central angle | 73810856 | |
| 73810857 | Semicircle | An arc, where a segment between its endpoints forms a diameter | 73810857 | |
| 73810858 | Congruent Arcs | Arcs with equal measure that lie in the same circle or in congruent circles | 73810858 | |
| 73810859 | Arc Addition Postulate | The measure of adjacent non-overlapping arcs is the sum of the measures of its two arcs. | 73810859 | |
| 73810860 | Congruent Chords and Arcs Theorem | In a circle or in congruent circles, congruent chords have congruent minor arcs | 73810860 | |
| 73810861 | Converse of Congruent Chords and Arcs Theorem | In a circle or in congruent circles, congruent minor arcs have congruent chords and congruent central angles | 73810861 | |
| 73810862 | Proof of Congruent Chords and Arcs Theorem | 1) Given, 2) Radii are congruent, 3) SSS postulate, 4) CPCTC, 5) Central angles are congruent to their intercepted arcs, 6) Substitution | 73810862 | |
| 73810863 | CPCTC | corresponding parts of congruent triangles are congruent | 73810863 | |
| 73810864 | Perpendicular Chord Theorem | If a diameter is perpindicular to a chord, then it bisects the chord and its major and minor arcs | 73810864 | |
| 73810865 | Converse of the Perpendidicular Chord Theorem | If a diameter bisects a chord that is not a diameter, then it is perpendicular to the chord and bisects its minor and major arcs | 73810865 | |
| 73810866 | Theorem | The perpendicular bisector of a chord contains the center of the circle | 73810866 | |
| 73810867 | Equidistant Chords Theorem | In the same circle or in congruent circles, congruent chords are equidistant from the center | 73810867 | |
| 73810868 | Converse of the Equidistant Chords Theorem | In the same circle or in congruent circles, chords equidistant from the center are congruent | 73810868 | |
| 73810869 | Inscribed Angle | An angles with a vertex on the circle and sides that contain chords of the circle | 73810869 | |
| 73810870 | Inscribed Angle Theorem | The measure of an inscribed angle is half the measure of its intercepted arc | 73810870 | |
| 73810871 | Corollary (of the Inscribed Angle Theorem) | If two inscribed angles intercept the same arc, then the angles are congruent | 73810871 | |
| 73810872 | Corollary (of the Inscribed Angle Theorem) | If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary | 73810872 | |
| 73810873 | Corollary (of the Inscribed Angle Theorem) | An angle inscribed in a semicircle is a right angle, and if an inscribed angle is a right angle, its intercepted angle is a semicircle | 73810873 | |
| 73810874 | Theorem | The measure of a tangent-chord angle is half the measure of its intercepted arc | 73810874 | |
| 73810875 | Two Chords Angle Theorem | The measure of an angle formed by two chords intersecting inside a circle is equal to half the sum of the intercepted arcs | 73810875 | |
| 73810876 | Secants-Tangents Angle Theorem | The measure of an angle formed by two secants, two tangents, or a secant and a tangent, drawn from a point outside the circle is equal to half the difference of the measures of its intercepted arcs. | 73810876 | |
| 73810877 | Chord Segment Theorem | If two chords intersect in a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the seconds chord | 73810877 | |
| 73810878 | Secant Segments Theorem | If two secant segments are drawn to a circle from an exterior point, then the product of one secant and its external segment equals the product of the lengths of the other secant segment and its external segment | 73810878 | |
| 73810879 | Secant/Tangent Segment Theorem | If a tangent segment and a sencant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment equals the product of the lengths of the secant segment and its external segment | 73810879 | |
| 73810880 | Area of a parallelogram | A=bh | 73810880 | |
| 73810881 | Area of a Triangle | A=½bh | 73810881 | |
| 73810882 | Area of a Trapezoid | A=½×h×(b₁+b₂) | 73810882 | |
| 73810883 | Area of a Quadrilateral with Perpendicular Diagonals | A=½×d₁×d₂ | 73810883 | |
| 73810884 | Apothem | The distance from the center of a regular polygon to its side | 73810884 | |
| 73810885 | Area of a Regular Polygon | A=½AP (where A is the apothem and p is the perimeter) | 73810885 | |
| 73810886 | Theorem | If two polygons are similar, then the ratio of their perimeters equals the ratio of any pair of corresponding segments | 73810886 | |
| 73810887 | Theorem | If two polygons are similar, then the ratio of their areas equals the squared ratio of any pair of corresponding segments | 73810887 | |
| 73810888 | Segments | Can mean sides, radii, apothems, altitudes, medians, and diagonals | 73810888 | |
| 73810889 | Circumference Ratio Theorem | The ratio C÷D of the circumference C to the diameter D is the same for all circles (π). Basically, C=πD. | 73810889 | |
| 73810890 | Arc Length Theorem | The ratio of the length of an arc of a circle (l) to the circumference (C) equals the ratio of the degree measure of the arc (the measure equaling m) to 360, so: l÷C=m÷360 | 73810890 | |
| 73810891 | Area of a Circle | A=πr² | 73810891 | |
| 73810892 | Area of a Sector | A=(m÷360)(πr²) | 73810892 | |
| 73810893 | Segment of a Circle | The region formed by an arc and its chord A=[area of the sector]-[area of the triangle] | 73810893 | |
| 73810894 | Volume | The number of cubic units contained in a solid | 73810894 | |
| 73810895 | Volume of a Prism | V=bh, where b is the area of the base and h is the height | 73810895 | |
| 73810896 | Volume of a Cylinder | V=bh, so V=πr²×h | 73810896 | |
| 73810897 | Volume of a Cone/Pyramid | V=1/3bh, where b is the area of the base and h is the height | 73810897 | |
| 73810898 | Volume of a sphere | V=4/3πr² | 73810898 | |
| 73810899 | Surface Area of Prisms | SA=ph+2b, where p is the perimeter of the base, h is the height, and b is the area of the base | 73810899 | |
| 73810900 | Surface Area of Cylinders | SA=ph+2b, where p is the perimeter of the base, h is the height, and b is the area of the base, So... SA=2rh+2πr² | 73810900 | |
| 73810901 | Regular Pyramid | A pyramid whose base is a regular polygon and lateral edges are congruent | 73810901 | |
| 73810902 | Slant Height | Height of any of the lateral faces (≠lateral edge) | 73810902 | |
| 73810903 | Surface Area of a Pyramid | SA=½pl+B | 73810903 | |
| 73810904 | Surface Area of a Cone | SA=½pl+B, so SA=πrl+πr² | 73810904 | |
| 73810905 | Surface Area of a Sphere | SA=4πr² | 73810905 | |
| 73810906 | Edge/Segment Ratio | In similar solids-A:B | 73810906 | |
| 73810907 | Area Ratio | In similar solids-A²:B² | 73810907 | |
| 73810908 | Volume Ratio | In similar solids-A³:B³ | 73810908 |
