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Geometry Review

Geometry Review. A. B. This is an example of a line . A line is usually represent by 2 arrowheads to indicate the line extends without and end. The points on the line help to identify it. A line extends in one dimension. Chapter One. Line AB.

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Geometry Review

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  1. Geometry Review

  2. A B This is an example of a line. A line is usually represent by 2 arrowheads to indicate the line extends without and end. The points on the line help to identify it. A line extends in one dimension. Chapter One Line AB Point A and Point B are collinear points, which are points that lie on the same line. K This an example of a plane. A plane is usually represented by a shape that looks like a table top or a wall. Even though the drawing makes it seem as though it has edges, you must imagine that it has no end. A plane extends in two dimensions. L M N Plane KLMN Points K, L, M, and N are all coplanar points, which are points that lie on the same plane.

  3. Distance Formula Chapter One A Point A(x ,y ) and Point B (x ,y ) are points in a coordinate plane, then the distance between A and B is: 1 1 2 2 B Perimeter, Circumference and Area Formulas c a P= a +b +c A=½bh s h P= 4s A=sˆ2 b Square (side- s) Triangle sides- a,b,c base-b height-h P= 2L + 2W A= LW L r C= 2r A= (rˆ2) W Circle radius- r Rectangle length-L width-W

  4. Chapter One This is an example of an angle. It could be named either angle BAC or angle CAB. The middle letter in the angle name is always the vertex. B vertex sides C A Classification of Angles This is an obtuse angle. An obtuse angle has a measure more than 90 but less than 180 degrees. This is a right angle. A right angle has a measure of 90 degrees, exactly. This is an acute angle. An acute angle has a measure less than 90. This is a straight angle. A straight angle has a measure of exactly 180 degrees.

  5. The Midpoint Formula Chapter One To find the midpoint of a segment, you must take the average/mean of the x-coordinates and of the y-coordinates. Vertical Angles Two angles are vertical angles when their sides form two pairs of opposite rays. In the figure to the left: 4  2 3  1 Linear Pairs Two adjacent angles are a linear pair if their non-common sides are opposite rays. In the figure to the left: 1  2

  6. Chapter Three Alternate Exterior Angles Two angles are alternate exterior angles if they lie outside two lines on opposite sides of the transversal. In this figure, 1 & 7 are alternate exterior angles. Alternate Interior Angles Two angles are alternate interior angles if they lie between the two lines on apposite sides of the transversal. In this figure, 4 & 6 are alternate interior angles.

  7. Chapter Three Consecutive Interior Angles Two angles are consecutive interior angles if they lie between two lines on the same side of the transversal. In this figure, 4 & 5 are consecutive interior angles. Corresponding Angles Two angles are corresponding angles if they occupy corresponding positions. In this figure, 1 & 5 are corresponding angels.

  8. Chapter Three Formula for the Slope of Parallel Lines In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. Formula for the Slope of Perpendicular Lines In a coordinate plane, two non-vertical lines are perpendicular if and if the produce of their slopes is -1. Vertical and horizontal lines are perpendicular.

  9. Classification of Triangles by Their Sides Chapter Four 3 congruent sides Equilateral Triangle 2 congruent sides Isosceles Triangle no congruent sides Scalene Triangle

  10. Classification of Triangles by Their Angles Chapter Four 1 right angle 3 acute angles Scalene Triangle Right Triangle 3 congruent angles 1 obtuse angle Equiangular Triangle Obtuse Triangle

  11. Chapter Four Triangle Sum Theorem C m A + m B +m C = 180 A B C Exterior Angle Theorem m1 = m A + m B 1 A B Corollary Theorem C m A + m B = 90 B A

  12. Polygon… is a plane figure that meets the following requirements: Chapter Six • A regular polygon is both equilateral and equiangular. 1) It’s formed by three or more segments called sides, such that no two sides with a common endpoint are collinear. 2) Each side intersects exactly two other sides, one at each endpoint. Convex Polygon… if no line that contains a side of the polygon contains a point in the interior of the polygon. Concave Polygon… a polygon that is not convex.

  13. Chapter Seven Reflection Line of Reflection Rotation Point of Rotation Translation Pre-image Image

  14. Chapter Eight If a and b are two quantities that are measured in the same units, then the ratio of a to b is written as a:b or a/b Cross Product Property A B C D If Then AD = BC = Reciprocal Property A B C D B A D C If = Then =

  15. Chapter Nine Pythagorean Theorem a +b =c 2 2 2 c The sum of the square of each leg is equal to the square of the hypotenuse. The hypotenuse is only in a right triangle and is the leg opposite of the right angle. a b 45-45-90 Triangle Theorem In a 45-45-90 triangle, the hypotenuse is √2 times as long as each leg. x : x : x√2 Trigonometric Ratios opposite Sin = hypotenuse adjacent 30-60-90 Triangle Theorem Cos = hypotenuse In a 30-60-90 triangle, they hypotenuse is two times as long as the shorter leg and the longer leg is √3 times longer than the shorter leg. x : x√3 : 2x opposite Tan = adjacent

  16. Chapter Ten Circleis the set of all points in a plane that are equidistance from a given point called the centerof a circle. • Radiusis the distance from a point on the circle to the center. • two circles are congruent • when they have the same • radius. Diameteris the distance from one point on the circle to another and passes through the center. radius . Center diameter

  17. Chapter Ten Chord is a segment whose endpoints are points on the circle. Secant is a line a that intersects a circle in two points. Tangent is a line in the plane of a circle that intersects in the circle at exactly one point.

  18. Chapter Ten A minor arc of a circle is formed by a central angle less than 180. A semicircle is formed by the endpoints of the diameter of a circle. A major arc of a circle is formed by a central angle more than 180.

  19. Chapter Eleven Polygon Interior Angles Theorem 11.1: The sum of the measures of the interior angles of a convex n-gon is (n-2)180. Corollary: The measure of each interior angle of a regular n-gon is (1/n)(n-2)180. Polygon Exterior Angles Theorem 11.2: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360. Corollary: The measure of each exterior angle of a regular n-gon is (1/n)360.

  20. Chapter Eleven Area of an Equilateral Triangle The area of an equilateral triangle is one fourth the square of the length of the side times the square root of three. A = (¼)(√3)(sˆ2) s Area of a Regular Polygon The area of a regular n-gon with side length s is half the product of the apothem a and the perimeter P, so A= (½)aP P=number of sides x side length s s a s

  21. Chapter Eleven . Arc Length A In a circle the ratio of length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360. . P . B arc length of AB 2r m AB 360 = Area of a Sector . A The ratio of a the area A of a sector of a circle to the area of a circle is equal to the ratio of the measure of the intercepted arc to 360. . P . B A rˆ2 m AB 360 =

  22. ChapterTwelve Polyhedron… is a sold that is bound by polygons, called faces, that enclose a single region of space. face . A vertex of a polyhedron is a point where three or more edges meet. An edge of a polyhedron is a line segment formed by the intersection of two faces.

  23. THE END Jaclyn A. Disharoon Pd. 1

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