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Geometry Final Exam Topics Chapter 1: Definitions: point, line, plane, space, line segment, ray, opposite rays, collinear, coplanar, postulate, theorem, congruent, midpoint, segment bisector, angle, acute, right, obtuse, straight angles, congruent angles, adjacent angles, and angle bisector Topics: Segment addition postulate Angle addition postulate Through any 2 points there is exactly one line. Through any 3 noncollinear points there is exactly one plane. If two planes intersect, they form a line. Pages to look at: 16, 22 Chapter 2: Definitions: conditional statements, hypothesis, conclusion, converse, biconditional statements, vertical angles, supplementary, complementary, perpendicular lines. Topics: Algebraic Properties (addition, subtraction, multiplicative, division, substitution, reflexive, symmetric, transitive) Midpoint Theorem Angle Bisector Theorem Complementary and Supplementary angle theorems Vertical angles are congruent Perpendicular line theorems on pg. 56 Pages to look at: 52-53, 58 Chapter 3: Definitions: Parallel lines, skew lines, transversal, alternate interior angles, same-side interior angles, corresponding angles, triangles, scalene, isosceles, equilateral, acute, obtuse, right, equiangular, polygon, regular polygon, inductive and deductive reasoning. Topics: Corresponding angles are congruent Alternate interior angles are congruent Same-side interior angles are supplementary Sum of measures of angles of a triangle is 180 degrees. Sum of measures of interior angles of a polygon is (n-2)180 Sum of measures of exterior angles of polygon is 360 degrees Pages to look at: 81, 86-87, 97,104 Chapter 4: Definitions: median of a triangle, altitude, and perpendicular bisector Topics: Corresponding Parts of Congruent Triangles are Congruent (CPCTC) ASA, SSS, SAS, AAS, HL Isosceles triangle theorem Parts of Isosceles Triangle Equilateral triangles are also equiangular. Page to look at: 137 Chapter 5: Definitions: Parallelogram, rectangle, rhombus, square, trapezoid, median of trapezoid, parts of trapezoid, and isosceles trapezoid. Topics: Properties of parallelograms Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other Properties of special quadrilaterals Parallel line theorems on pg. 177-78 Find length of median of a trapezoid Pages to look at: 169-170, 175, 180-181, 187, 192 Chapter 6: Topics: Inequalities in a triangle. Triangle Inequality Theorem Pages to look at: 221-223 Chapter 7: Definitions: ratio, proportion, similar, and scale factor Topics: Properties of proportions AA Similarity Postulate SSS Similarity Theorem SAS Similarity Theorem Corollary on pg. 270 Pages to look at: 243-244, 247, 251, 257, 266, 272 Chapter 8: Definitions: parts of a right triangle, sine, cosine, and tangent ratios Topics: Pythagorean Theorem Special Right Triangles – 45,45,90 and 30, 60, 90 Sin, Cos, and Tan ratios Angle of depression and angle of elevation Pages to look at: 292-293, 297, 301, 302, 308, 314-315, 319 Chapter 13: Topics: Distance between 2 points d y y1 Slope m 2 x 2 x1 x x2 y1 y 2 , Midpoint 1 2 2 Pages to look at: 526,532,545 x2 x1 2 y2 y1 2 Chapter 11: Topics: Find perimeter and area of rectangle, square, parallelogram, triangle, and trapezoid. Find circumference and area of circles. Pages to look at: 426,431,436-437, 448-449 Chapter 12: Topics: Find surface area of rectangular prisms, spheres, cones, and cylinders. Find volume of rectangular prisms, spheres, cones, and cylinders. Look at: formula sheet, surface area and volume review worksheets Chapter 9: Definitions: Circle, center, radius, diameter, secant, chord, tangent line, point of tangency, sphere, arc, major and minor arcs, semicircle, central angles, inscribed angles, congruent circles, and concentric circles. Topics: A line tangent to a circle is perpendicular to radius at the point of tangency. Central angle measure = arc measure Inscribed angle measure = ½ arc measure Congruent arcs have congruent chords Congruent chords are equidistant from the center. Measure of the angle formed by a chord and a tangent line is ½ the measure of the arc Diameter is perpendicular to a chord then it bisects the chord and the arc. If a quadrilateral is inscribed in a circle, then opposite angles are supplementary. The measure of an angle formed by two chords that intersect inside a circle is equal to ½ the sum of the intersected arcs. The measure of an angles formed by two secants or tangents is equal to ½ the difference of the intercepted arcs. Pages to look at: 341, 347, 354, 358-359