56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

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1 6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S ) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit diagnostics are particularly helpful because they are a form of "pretest" that you can use to assess your performance and prescribe topics for review. Study the unit wrap-ups. Read each unit wrap-up to determine which topics you need to review further. Review important vocabulary terms. Study the key terms listed on the next page to identify any vocabulary you don't know. Use the "Check Your Understanding" pages and math workbook assignments as study aids. Review the "Check Your Understanding" pages to get right, wrong, and hint feedback to specific math problems. The math workbook assignments you've completed throughout the semester will also provide you with a great review for the exam. Review the activities that contain information you need to review further. After determining which topics are least familiar to you, review the activity in which they are covered. This could include revisiting study activities and rereading math workbook assignments. Taking the Semester Exam For all exam questions Read the entire question and all the choices before selecting an answer. Then choose the best answer or answers. Semester Exam 56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

2 Semester Review: Geometry, Semester 2 Semester Key Terms altitude apothem arc area axes Cartesian coordinate system center chord circle circumcenter circumference circumscribe concave cone congruent polygons convex cylinder decagon deviation diagonal diameter distance formula dodecagon dodecahedron exterior angle heptagon hexagon hexahedron icosahedron incenter interior angle inscribe inscribed angle intersecting chord theorem irrational number latitude linear equation linear relationship line of best fit longitude major arc midpoint oblique pyramid octagon octahedron ordered pair origin parallel parallelogram pentagon perimeter π Platonic solid point-slope equation polygon polyhedron positive correlation prisms pyramids Pythagorean theorem quadrilateral radius rate of change rectangle regular polygon René Descartes right pyramid secant sector similar polygons slope slope-intercept equation sphere surface area tangent tetrahedron triangle x-axis x-coordinate xy-plane y-axis y-coordinate y-intercept

3 midpoint formula minor arc negative correlation negative reciprocals n-gon nonagon

4 Key Terms and Concepts for Unit 6 (1) Unit 6 Key Terms altitude apothem area concave congruent polygons convex decagon diagonal dodecagon exterior angle heptagon hexagon interior angle n-gon nonagon octagon parallelogram pentagon perimeter polygon quadrilateral rectangle regular polygon similar polygons triangle (Definition) Know that a polygon is a closed figure whose sides are line segments. (Definition) Know that the perimeter of a polygon is the distance around the polygon. (Definition) Know that a quadrilateral is a polygon with four sides. Know the names of common polygons: Number of Sides n Name of Polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon n-gon Know how to name a polygon. (List the vertex labels in order clockwise or counterclockwise.) The quadrilateral below can be named BCED, CEDB, EDBC, DBCE, BDEC, DECB, ECBD, or CBDE.

5 (Definition) Know that a convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. A concave polygon is a polygon such that two or more lines containing a side of the polygon contain a point in the interior of the polygon. (Definition) A regular polygon is a convex polygon with all sides congruent and all angles congruent. (Definition) Know that congruent polygons have the same size and shape. (Definition) Know that similar polygons have the same shape but not necessarily the same size. (Definition) Know that a diagonal is a segment that connects two nonconsecutive vertices of a polygon. Know that the sum of the measures of the interior angles of a polygon with n sides is (n - 2)180. Name of Polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon n-gon Number of Sides n Sum of Measures of Interior Angles ,080 1,260 1,440 (n - 2)180 Know that the measure of each interior angle of a polygon with n sides is. (Definition) Know that an exterior angle of a polygon is an angle that forms a linear pair with one of the polygon's interior angles. (Theorem) Know that the sum of the measures of the exterior angles of any convex polygon is 360.

6 (Definition) Know that a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. (Theorem) Know that opposite sides of a parallelogram are congruent. (Theorem) Know that opposite angles in a parallelogram are congruent. (Theorem) Know that consecutive angles in a parallelogram are supplementary. (Theorem) Know that the diagonals of a parallelogram bisect each other. (Theorem) Know that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. (Theorem) Know that if one pair of opposite sides of a quadrilateral is parallel and congruent, then the quadrilateral is a parallelogram. (Theorem) Know that if consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. (Theorem) Know that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. (Definition) Know that a rectangle is a quadrilateral with four right angles. Know that all rectangles are parallelograms. (Theorem) Know that the diagonals of a rectangle are congruent. (Theorem) Know that if a parallelogram has a right angle, then it is a rectangle. (Theorem) Know that if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. (Definition) Know that a rhombus is a quadrilateral with four congruent sides. (Theorem) Know that the diagonals of a rhombus are perpendicular. (Theorem) Know that each diagonal of a rhombus bisects a pair of opposite angles. (Theorem) Know that if a parallelogram has two adjacent sides congruent, then it is a rhombus. (Definition) Know that a square is a quadrilateral with four right angles and four congruent sides.

7 (Definition) Know that a trapezoid is a quadrilateral with exactly one pair of parallel sides. (Definition) Know that the parallel sides of a trapezoid are called its bases. (Definition) Know that the nonparallel sides of a trapezoid are called its legs. (Definition) Know that the intersection of a base with a leg forms a base angle. (Definition) Know that an isosceles trapezoid is a trapezoid with congruent legs. (Theorem) Know that both pairs of base angles of an isosceles trapezoid are congruent. (Theorem) Know that the diagonals of an isosceles trapezoid are congruent. (Definition) Know that the median of a trapezoid is the segment that joins the midpoints of the legs. (Theorem) Know that the median of a trapezoid is parallel to the bases and its length is equal to half the sum of the lengths of the bases. Know that the perimeter of a parallelogram with length l and width w is calculated as follows: P = 2l + 2w Know that the perimeter of a rhombus or square with side lengths s is calculated as follows: P = 4s (Definition) Know that the area of a polygon is the number of square units contained in its interior. Know that the area of a rectangle with length l and width w is calculated as follows: A = lw Know that the area of a square with side length s is calculated as follows: A = s 2 Know that an altitude of a parallelogram is a segment from one vertex that is perpendicular to the opposite side. Know that the height of a parallelogram is the length of its altitude. Know that the area of a parallelogram with base b and height h is calculated as follows: A = bh Know that the area of a rhombus with diagonals of length d1 and d2 is calculated as follows:

8 Know that the area of a trapezoid with bases of length b1 and b1 and height h is calculated as follows: (Definition) Know that the area of a polygon is the number of square units contained in its interior. Know that the distance from the center of the polygon to a side is measured by the apothem. Review Unit 6, Lesson 9 for an illustration of an apothem. Know that the area of a regular polygon with perimeter P and apothem length a is given by:

9 Key Terms and Concepts for Unit 7 (2) Unit 7 Key Terms arc center chord circle circumcenter circumference circumscribe diameter incenter inscribe inscribed angle intersecting chord theorem irrational number major arc minor arc π radius secant sector tangent (Definition) Know that a circle is the collection of points in a plane that are the same distance from a given point in the plane. (Definition) Know that all of the points on a circle are the same distance from the center. (Definition) Know that a radius is a segment that connects any point on a circle to the center of that circle. (Definition) Know that the radius of a circle is the length of any of its radii. (Definition) Know that the distance around a circle is called the circumference. (Definition) Know that a chord of a circle is a line segment whose endpoints are on the circle. (Theorem) Know that if two chords are the same distance from the center of a circle, then they are congruent. (Theorem) Know that if two chords are congruent, then they are the same distance from the center of the circle that contains them. (Theorem) Know that if a radius of a circle is perpendicular to a chord, then it bisects that chord. (Definition) Know that a diameter is a chord that passes through the center of the circle. (Definition) Know that the diameter of a circle is the length of any diameter that the circle contains. (Definition) Know that an arc is a connected piece of a circle.

10 Know that to label the major arc joining A and B, you use an intermediate point in the label so that you don't confuse the major and minor arcs. The minor arc below is named arc AB, and the major arc is named arc AXB. (Definition) Know that the measure of a minor arc arc AB, written mab, is the measure of the central angle that intercepts the arc. (Definition) Know that the measure of a major arc is 360 minus the measure of the minor arc with the same endpoints. (Definition) Know that two arcs are congruent if they have the same measure and also belong to the same circle or to congruent circles. (Theorem) Know that two arcs of a circle are congruent if and only if their central angles are congruent. (Theorem) Know that two arcs of a circle are congruent if and only if their associated chords are congruent. (Theorem) Know that two chords are congruent if and only if the associated central angles are congruent. (Definition) Know that an inscribed angle is an angle formed by two chords that share an endpoint. (Theorem) Know that the measure of an inscribed angle is half the measure of the intercepted arc. (Intersecting chord theorem) Know that the measure of an angle formed by intersecting chords is half the sum of measures of the intercepted arcs. (Definition) Know that a secant is a line or segment that passes through a circle in two places.

11 (Theorem) Know that the measure of a secant-secant angle is half the difference of the measures of the intercepted arcs. (Definition) Know that a tangent line is a line that intersects a circle at exactly one point. (Definition) Know that a point of tangency is a point at which a tangent line meets a circle. (Definition) Know that any segment of a tangent line that contains the point of tangency is called a tangent segment. (Theorem) Know that a tangent is perpendicular to the radius that shares the point of tangency. (Theorem) Know that the measure of a tangent-tangent angle is half the difference of the measures of the intercepted arcs. (Theorem) Know that the measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle. (Definition) Know that the distance around a circle is called the circumference. Know that the formula for circumference is: C = 2πr, where r is the radius of the circle. Know that π is an irrational number, which means that its digits go on forever without any pattern. Know that the length of an arc can be calculated with the following formula: Know that the area of a circle can be computed with the following formula: area = πr 2 (Definition) Know that a sector of a circle is a region bounded by an arc of a circle and radii to the endpoints of the arc. Know that you can calculate the area of a sector using the following formula: Know that when you draw a circle inside a triangle so that each side of the triangle is tangent to the circle, you inscribe the circle. Know that the center of a circle that's inscribed in a triangle is the triangle's incenter.

12 Know that the incenter of a triangle is always at the intersection of the bisectors of the triangle's angles. Also, the incenter is equidistant from the triangle's sides, and it is always inside the triangle. Know that when you draw a circle around a triangle so that each vertex of the triangle is on the circle, you circumscribe the circle about the triangle. Know that the center of a circle circumscribed about a triangle is called the triangle's circumcenter. Know that the circumcenter of a triangle is always at the intersection of the perpendicular bisectors of the triangle's sides. The circumcenter is equidistant from the vertices of the triangle. The cirumcenter of a right triangle is on the side opposite the right angle. The circumcenter of an obtuse triangle is outside of the triangle. Know that the incenter of a polygon is the center of the inscribed circle. Know that the circumcenter of a polygon is the center of the circumscribed circle. (Theorem) Know that the opposite angles of a quadrilateral in a circumscribed circle are supplementary. (Theorem) Know that a parallelogram in a circumscribed circle must be a rectangle.

13 Key Terms and Concepts for Unit 8 (3) Unit 8 Key Terms axes Cartesian coordinate system deviation distance formula latitude linear equation linear relationship line of best fit longitude midpoint midpoint formula negative correlation negative reciprocals ordered pair origin parallel point-slope equation positive correlation Pythagorean theorem rate of change René Descartes slope slope-intercept equation x-axis x-coordinate xy-plane y-axis y-coordinate y-intercept Know that latitude specifies how far north a point on the globe is. Longitude specifies how far east a point is on the globe. Know that the Cartesian coordinate system is composed of two intersecting number lines called the axes. The point where the axes intersect is called the origin. Know that the horizontal axis is usually labeled the x-axis and the vertical axis is usually labeled the y-axis. A Cartesian coordinate system with an x- and a y-axis is called an xy-plane. Know that the location of a point on the xy-plane is specified by two coordinates. The number on the x-axis that lines up with a point is the point's x-coordinate and the number on the y-axis that lines up with a point is the point's y-coordinate. (Definition) Know that an ordered pair is an x-coordinate and then a y-coordinate in parentheses. An ordered pair describes the location of a point on a plane. (Definition) The midpoint of a segment is the point halfway between its endpoints. Know that the formula for the midpoint of a segment is: (Theorem) Know the Pythagorean theorem: If a and b are the lengths of the legs of a right triangle, then the hypotenuse, c, can be found with the following formula: c 2 = a 2 + b 2

14 Know that the distance, d, between the points (x2, y2) and (x2, y2) is given by the distance formula: Know that when the points on a graph tend to be higher the farther right they are, they indicate a positive correlation. Know that when the points on a graph tend to be lower the farther right they are, they indicate a negative correlation. Know that if the points are scattered randomly, they indicate no correlation. Know that the value measured by the horizontal axis is called the independent variable. The value measured by the vertical axis is called the dependent variable. Know that the line of best fit will always go through the middle of the data points. Know that the farther data points are from the line of best fit, the greater the deviation. (Definition) A linear equation is an equation whose graph is a straight line. Know how to use the line of best fit to make predictions. Know how to use the equation for the line of best fit to make predictions. Review Unit 8, Lesson 5 for more. (Definition) Know that: Know how to calculate the slope of a line using the following formula: Know that horizontal lines have a slope of zero, and vertical lines have undefined slope. Know that slope measures the rate of change of the y-variable with respect to the x-variable. Know that two lines are parallel if they have the same slope. Two lines are perpendicular if they have slopes that are negative reciprocals of each other. Two numbers are negative reciprocals if their product is 1. Know that the point at which a line crosses the y-axis is called the line's y-intercept. Know the slope-intercept equation: y = mx + b, where m is the slope of the line and b is the y-coordinate of the line's y-intercept.

15 Know the point-slope equation: (y - y0) = m(x - x0), where m is the slope of the line and (x0, y0) is a point on the line. Know the equation of a circle centered at the origin: x 2 + y 2 = r 2, where r is the radius of the circle. Know the general equation of a circle: (x - h) 2 + (y - v) 2 = r 2

16 Key Terms and Concepts for Unit 9 (4) Unit 9 Key Terms cone cylinder dodecahedron hexahedron icosahedron oblique pyramid octahedron Platonic solid prisms polyhedron pyramids right pyramid sphere surface area tetrahedron (Definition) Know that a polyhedron is a solid bounded by the polygonal regions formed by intersecting planes. (Definition) Know that a prism is a solid consisting of two parallel congruent polygons and all the points between them. (Definition) A pyramid is a solid consisting of a polygon, a point not in the same plane as the polygon, and all the points between them. Know that in a right pyramid, the vertex is directly over the center of the polygon. In an oblique pyramid, the vertex is not directly above the center of the polygon. (Definition) A cylinder is a solid made from two parallel congruent disks and all the points between them. (Definition) A cone is a solid made from a disk, a point not in the same plane as the disk, and all the points between them. Know that in a right cone, the vertex is directly over the center of the disk. In an oblique cone, the vertex is not directly above the center of the disk. Know that a Platonic solid is a solid every face of which is the same regular polygon. Know that a tetrahedron has 4 faces, each of which is an equilateral triangle. Know that a hexahedron (cube) has 6 faces, each of which is a square. Know that an octahedron has 8 faces, each of which is an equilateral triangle. Know that a dodecahedron has 12 faces, each of which is a regular pentagon. Know that an icosahedron has 20 faces, each of which is an equilateral triangle.

17 Know that the lateral area of a right prism is given by the following formula: LA = ph, where p is the perimeter of the base and h is the prism's height. Know that the surface area of a right prism is given by the formula: surface area = BA + LA = BA + ph, where BA is the area of the prism's bases, p is the perimeter of the bases, and h is the height of the prism. Know that the lateral area of a regular pyramid can be found using the following formula:, where p is the perimeter of the base and s is the slant height of the pyramid. Know that the surface area of a regular pyramid can be found using the following formula: surface area = the slant height of the pyramid., where BA is the area of the base, p is its perimeter, and s is Know that the lateral area of a right cylinder can be found using the following formula: LA = (2πr)h, where r is the radius of the base and h is the height of the cylinder. Know that the surface area of a right cylinder can be found using the following formula: surface area = BA + LA = 2(πr 2 ) + (2πr)h, where r is the radius of the base and h is the height of the cylinder. Know that the lateral area of a right cone can be found using the following formula: LA = πrs, where r is the radius of the base and s is the slant height of the cone. Know that the surface area of a right cone can be found using the following formula: surface area = BA + LA = πr 2 + πrs, where r is the radius of the base and s is the slant height of the cone. Know that the volume of a prism can be found using the following formula: V = Bh, where B is the area of the base and h is the length of the prism's altitude. Know that the volume of a cylinder can be found using the following formula: V = Bh, where B is the area of the base and h is the height of the cylinder. Know that the volume of a pyramid can be found using the following formula:, where B is the area of the base and h is the height of the pyramid. Know that the volume of a cone can be found using the following formula:, where B is the area of the base and h is the height of the cone. (Definition) A sphere is a solid bounded by the set of all points at a given distance from a point.

18 Know that the surface area of a sphere can be found using the following formula: SA = 4πr 2, where r is the radius of the sphere. Know that the volume of a sphere can be found using the following formula:, where r is the radius of the sphere. Know that two solids are similar if their corresponding parts have equal ratios in all dimensions. All spheres are similar. Know that the ratio of the surface areas of two similar solids is equal to the square of the ratio between their corresponding edge lengths. Know that the ratio of the volumes of two similar solids is equal to the cube of the ratio between their corresponding edge lengths. Copyright 2012 Apex Learning Inc. (See Terms of Use at

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