Honors Geometry Second Semester Final Review This review is designed to give the student a BASIC outline of what needs to be reviewed for the second semester final exam in Honors Geometry. It is up to the individual student to determine how much extra work is required for concept mastery. Chapters : Geometric Shapes and Measurement (p. 35) 1). Points, Lines, and Planes Points, collinear points, lines, planes, coplanar ). Segments, Rays, Parallel Lines, and Planes 3). Measuring Segments 4). Measuring Angles Line segments, rays, opposite rays, parallel lines Examples found on page 46 # s 1,, 4-8 all Congruent segments Midpoint of a segment Angles, adding angles, subtracting angles, vertical angles, adjacent angles Complementary angles: Add = 90 o Supplementary angles: Add = 180 o Classify angles by size: acute, right, obtuse, and straight Examples found on page 47 # s 9-15 all, 17, 19, 3, 5 5). Angles of a Polygon Names of basic polygons page 55. Sum of the INTERIOR angles of an n-sided polygon: S n = (n - )180 Sum of the EXTERIOR angles: S e = 360 Regular Polygons : All sides, all angles Measure of 1 Interior angle = I Measure of 1 Exterior angle = E m(interior ) + m(exterior ) = 180 same as I + E = 180 The measure of ONE EXTERIOR angle is E = 360 n The number of sides/vertices is n = 360 E Examples can be found on Regular Polygons worksheet and page 7 # s 7-17, 19, 1 Chapter 3: Perimeter, Area, and Volume (p. 103) 1). Simple Radical Form: All answers on the exam will be in this form unless otherwise specified!!!!!!! ). Pythagorean Theorem: a + b = c 3). Special Right Triangles: 30-60-90 Triangles Hypotenuse = s Short Leg = Long Leg = Hypotenuse Long Leg Short Leg 45-45-90 Triangles Leg = s Hypotenuse = s Hypotenuse Leg Leg 1
4). Areas of polygons: square, rectangle, hexagon, triangles, equilateral triangles, and more! 5). Areas of Shaded Regions 6). Surface Area and Volume Prisms rectangular, triangular, hexagonal and others How to calculate SA and Volume Pyramids Slant height Lateral height Altitude/Height How to calculate SA and Volume Know how to calculate SA and volume for prisms, pyramids, cylinders, cones and spheres. Chapter 4: Triangle Congruence (p. 183) 1). Congruent Triangles: Have congruent corresponding parts o Their matching sides and angles are the same! When you name the polygons you MUST list the corresponding vertices in the same order. If ΔABC ΔDEF, then 1) all three pairs of corresponding angles are congruent, and ) all three pairs of corresponding sides are congruent. and ). Five ways to prove triangles are congruent SSS: Side-Side-Side SAS: Side-Angle-Side; The angle MUST be between the two sides. ASA: Angle-Side-Angle; The side MUST be between the two angles. HL Thm: Hypotenuse-Leg Congruence Thm; ONLY used with RIGHT triangles. LL Thm: Leg-Leg Congruence Theorem; ONLY used with RIGHT triangles. 3). Congruent Triangles: CPCTC: Corresponding Parts of Congruent Triangles are Congruent be sure to label triangles in the correct order the vertices(angles) line up and the sides line up 4). Isosceles Triangles: If angles then sides If sides then angles Chapter 5: Parallel Lines and Quadrilaterals (p. 37) 1). Definitions Parallel lines ll, Skew lines, Parallel planes, Transversals, Alternate Interior Angles AIA, Alternate Exterior Angles AEA, Same-Side Interior Angles SSIA, Corresponding Angles Corr s ). Properties of Parallel Lines ll lines corrs s ll lines AIA ll lines AEA ll lines SSIA supp Parallel Postulate Crook Problems 3). Miscellaneous Facts Exterior Angle Theorem m4 = m1 + m 1 4
Angle Bisector Theorem A point on the angle bisector is equidistant from the sides of the angle. 4). Properties of the following quadrilaterals: Parallelograms, rhombus, rectangle, square, trapezoids, and isosceles trapezoids Chapter 6: Similarity : pages 95-358 1). Ratios and Proportions (p. 95) Ratios: Simplify and leave in improper fraction form ). Similar Triangles (p. 307) corresponding angles are congruent the ratios of the lengths of corresponding sides are proportional the ratio of the perimeters is equal to the ratio of corresponding sides scale factor = ratio of corresponding sides = ratio of perimeters AAA, LL (Right Triangles only!) These are more popular: AA, SSS, SAS 3). Similarity in Right Triangles (p. 30) Geometric Mean 4). Know the following theorems: Side-Splitter Theorem, Midsegment Theorem, Lefty-Righty Theorem, and the Midsegment Theorem 5). Right Triangle Trigonometry SOH CAH TOA 6). Laws of Trigonometry Law of Sines and the Law of Cosines Chapter 7: Circles (p. 359) 1). You should be able to label and identify the following: Radius, diameter, Secant, Tangent, Point of Tangency, Chord, Central Angle, Minor Arc, Major Arc, Semi-Circle, Congruent Arcs ). Segments drawn from the center of a circle to a chord: If then bisects If bisects then 3). Congruent Chord Stuff : If equidistant then congruent If congruent then equidistant 4). Basic properties of arcs : congruent cords congruent arcs congruent central angles 5). Secants and tangents A radius drawn to a tangent line is perpendicular to it. 6). Angles related to a circle Central Angle, Vertex On, Vertex Inside, Vertex Outside 7). The power theorems : Chord-Chord, Tangent-Secant, Secant-Secant 3
Moise-Downs Trig Unit 1). Radian Measure, Conversions, and the Unit Circle. The Unit Circle To convert from degrees to radians or radians to degrees, use the proportion To convert from degrees to radians, use: ( ) To convert from radians to degrees, use: ( ) Directed Angles: The order of the letters MATTERS! An angle is in standard position if it is drawn in the xy plane with its vertex at the origin and its initial side on the positive x axis. Positive Rotation and Negative Rotation ). Sum Formulas: Difference Formulas: cos( ) cos cos sin sin cos( a b) cos a cos b sin a sin b a b a b a b a b a b a b sin( a b) sin acos b cos asin b tan a tan b tan a tan b ab tan( ab) 1 tan a tan b 1 tan a tan b ( whenever tan a tan b 1) sin( ) sin cos cos sin tan( ) ( whenever tan a tan b 1) Fundamental Identities: ( ) Formulas: cos( ) cos Formulas: cos sin sin( ) sin sin cos Double Angle Formulas: sin sin cos cos cos sin cos 1sin tan 1 tan tan cos cos 1 3). Inverse trigonometric functions. 4). Area problems. Chapter 8: Coordinate Geometry (p. 419) 1). Coordinates and Distance in the Plane: (p. 419) The Distance Formula: P( x, y ) and Q( x, y ) are two points in the coordinate plane, then: If 1 1 The distance between P and Q = PQ ( x x ) ( y y ). 1 1 The Midpoint Formula: If P( x1, y 1) and Q( x, y ) are endpoints of a line segment, then the midpoint of PQ is x x y y 1 1 M,. 4
). Section 8.: Slope (p. 436) Slope of a Line: Remember: Horizontal Lines: Slope = 0 Vertical Lines: Infinite Slope or Undefined Slope Slopes of Parallel Lines Two lines in a coordinate plane are parallel if and only if: a. their slopes are equal, or b. their slopes are undefined = D.N.E. = Infinite Slope Slopes of Perpendicular Lines have opposite reciprocal slopes. 3). 8.3 Equations of Lines and Circles: Forms of Equations of Lines Point-slope form: y y m( x x ) 1 1 Slope-intercept form: y mx b Standard form: Ax By C Equation of a Circle The circle with center (h, k) and radius r has the equation: A circle with its center at the origin; (h, k)=(0,0) is given by: ( ) ( ) x h y k r. x y r Graphing Parabolas: General Form: y = ax + bx + c y-intercept is when x = 0 y = c Vertex of the parabola: (h,k) h = - b a k = ah + bh + c x-intercepts is when y = 0 Factor or use the quadratic formula Be able to solve for the points of intersection when you graph circles, parabolas, and lines! Section 9.1: Isometries and Congruence 1). A transformation of a geometric figure is a change in its position, shape, or size. The original figure is the preimage. The resulting figure is an image. An isometry is a transformation in which the image and preimage are congruent. Translations, rotations, reflections, and glide-reflections are isometries. ). Translations: moves every point of a figure the same distance in the same direction ( ), where a and b are constants. 5
3). Rotations: Positive rotations are counterclockwise. Negative rotations are clockwise. Angle of Rotation Mapping 90 o (-70 o ) 180 o 70 o (-90 o ) 4). Reflections: Line of Reflection Mapping x-axis y-axis y = x y = -x 5). Similitudes and Similarity Dilations: Are size transformations k = scale factor Polar Coordinates and Equations: (r, Ө) Polar-to-Rectangular: Rectangular-to-Polar: x = r cos(ө) therefore ( ) y = r sin(ө) Additional Topics: Perfect Rectangles Quadratic Equations and The Quadratic Formula Exponents Logarithm Rules 6