Download Partners for Student Success - Cecil County Public Schools

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