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Partners for Student Success Grade 8 Geometry Semester Unit 4: Patterns In order for your child to be successful, it is important to be consistent with the mathematical vocabulary and processes that will be implemented this year in Algebra. You may find this resource helpful when supporting your child at home. Unit Concepts Concept Explanation Circle The set of all points in a plane that are equidistant from a given point called the center. Chord A segment whose endpoints are on a circle. Secant A line that intersects a circle in two points. Tangent A line in the plane of a circle that intersects the circle in exactly one point. Central Angle An angle whose vertex is the center of a circle. Minor Arc Part of a circle that measures less than 180˚. Major Arc Part of a circle that measures between 180˚ and 360˚. Semi-Circle An arch with endpoints that are the endpoints of a diameter of a circle. (this arch always measures 180˚) Cecil County Public Schools 2014-15 Examples 1 Grade 8 Geometry Semester Unit 4 Partners for Student Success Congruent Circles Two circles that have the same radius. Congruent Arcs Two arcs that have the same measure and are arcs of the same circle or congruent circles. Inscribed Angle An angle whose vertex is on a circle and whose sides contain chords of a circle. Intercepted Arc The arc that lies in the interior of an inscribed angle and has endpoint on the angle. Standard Equation of a Circle Radius The standard equation of a circle with a center (2,3) and a radius 4 is: (x – 2)2 + (y – 3)2 = 16. (x h)2 (y k)2 r2 A segment whose endpoints are the center of the circle and a point on the circle. The distance from the center of a circle to any point on the circle. Half the measure of the diameter. Standard: y x 2 4 x 3 Intercept: y ( x 1)( x 3) Equivalent Equations Produce equivalent forms of quadratics using standard, intercept, and vertex form. Equation of a Circle Complete the square of the equation of a circle to find the center and radius. Trigonometric Ratio The ratio of the lengths of two sides in a right triangle. Sine Ratio The ratio of the lengths of the side opposite of an acute angle and the hypotenuse in a right triangle. Cosine Ratio The ratio of the lengths of the side adjacent to an acute angle and the hypotenuse in a right triangle. Tangent Ratio The ratio of the lengths of the legs in a right triangle. Cecil County Public Schools 2014-15 Vertex: y ( x 2) 2 1 x 2 y 2 18x 12 y 68 0 2 Grade 8 Geometry Semester Unit 4 Partners for Student Success Cotangent Ratio The reciprocal of tangent. The ratio of the length of the adjacent side to the length of the opposite side. Secant Ratio The reciprocal of cosine. The ratio of the length of the hypotenuse to the length of the adjacent side. Cosecant Ratio The reciprocal of sine. The ratio of the length of the hypotenuse to the length of the opposite side. Additional Resources www.corestandards.org o View the math standards your child will be learning this year. Scroll down and click “Mathematics Standards” to download the pdf document. www.ixl.com/math/standards/common-core o Click “High School” or “Eighth Grade” to find interactive practice opportunities aligned with each math standard. www.studyjams.com o Using the search bar, find interactive examples and opportunities for practice for any given concept. www.khanacademy.org o Using the search bar, find videos and examples on several math concepts throughout the year. http://www.shmoop.com/common-core-standards o Using the anchor standard, subtopic, and standard to unpack each standard. Cecil County Public Schools 2014-15 3 Grade 8 Geometry Semester Unit 4 Partners for Student Success