Honors Geometry CHAPTER 7. Study Guide Final Exam: Ch Name: Hour: Try to fill in as many as possible without looking at your book or notes.

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1 Honors Geometry Study Guide Final Exam: h 7 12 Name: Hour: Try to fill in as many as possible without looking at your book or notes HPTER 7 1 Pythagorean Theorem: Pythagorean Triple: 2 n cute Triangle (Theorem 73) : 3 n Obtuse Triangle (Theorem 74) : Triangle Triangle Theorem: Theorem: Tangent Ratio: Tan = 6 Sine Ratio: Sin = 7 osine Ratio: os = 8 Exact Values of Sine, osine, Tangent of 30, 45, 60 : sin 45 = cos 45 = tan 45 = sin 30 = cos 30 = tan 30 = sin 60 = cos 60 = tan 60 = 9 ngle of Elevation and ngle of Depression: Know how to identify them in a picture 10 Inverse Tangent: Use tan 1 to find m at the right 11 Inverse Sine: Use sin 1 to find m at the right Inverse osine: Use cos 1 to find m at the right 4 13 Law of osines: o Use Law of osines when the information in a picture forms a SS condition (or SSS condition) b 14 Law of Sines: a o Use Law of Sines when the information in a picture forms an S or a S condition c

2 HPTER 8 1 Polygon Interior ngles Theorem: The sum of the measures of the interior angles of a convex n-gon is page 2 of 8 2 Each interior angle of a regular n-gon has measure: 3 Polygon Exterior ngles Theorem: The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is 4 Definition of a Parallelogram: (mark the picture according to the definition) 5 If a quadrilateral is a parallelogram, then: Theorem 83: Theorem 84: Theorem 85: Theorem 86: 6 Ways to Prove a Quadrilateral is a Parallelogram: Theorem 87: If then the quadrilateral is a parallelogram Theorem 88: If then the quadrilateral is a parallelogram Theorem 89: If then the quadrilateral is a parallelogram Theorem 810: If then the quadrilateral is a parallelogram 7 Rhombus orollary: quadrilateral is a rhombus if and only if it has (mark the picture according to the corollary) 8 Rectangle orollary: quadrilateral is a rhombus if and only if it has (mark the picture according to the corollary) 9 Square orollary: quadrilateral is a rhombus if and only if it has (mark the picture according to the corollary) 10 Theorem 811: parallelogram is a rhombus if and only if its 11 Theorem 812: parallelogram is a rhombus if and only if 12 Theorem 813: parallelogram is a rectangle if and only if its

3 page 3 of 8 13 Definition of a trapezoid: (mark the picture according to the definition) Know the vocabulary of a trapezoid: bases, base angles, legs 14 Isosceles Trapezoid: trapezoid with 15 Theorem 814: If a trapezoid is, then 16 Theorem 815: If a trapezoid has a 17 Theorem 816: trapezoid is 18 Definition of a midsegment of a trapezoid: 19 Midsegment Theorem for Trapezoids: The midsegment of a trapezoid is to each and is 20 Definition of kite: (mark the picture according to the definition) 21 If a quadrilateral is a kite, then Theorem 818: Theorem 819: 22 Hierarchy: Draw the hierarchy of quadrilaterals HPTER 9 1 Isometry: transformation that 2 Vectors: Initial Point: Terminal Point: Horizontal omponent: G Vertical omponent: omponent Form: F

4 page 4 of 8 3 Point Matrix for (x,y): 4 dd/subtract Matrices: = Translations with Matrices: 2 by 3 matrix for translating a triangle 1 unit left and 4 units up is 6 Multiplying Matrices: = Scalar Multiplication: 4 = Reflection of P over line m: reflection over line m maps every point P in the plane to a point P, so that for each point one of the following is true: oordinate Rules for Reflections: If (x, y) is reflected over: The x-axis, its image is the point The y-axis, its image is the point The y = x, its image is the point The y = x, its image is the point 10 Reflection Matrices: 1 Reflection over the x-axis has matrix 2 Reflection over the y-axis has matrix 11 Isometry: Translation Rotation What does this isometry do to a figure? Number of reflections Reflected over what type of line(s)? Magnitude: enter: (does not apply) 12 oordinate Rules for Rotations about the Origin: When a point (x, y) is rotated counterclockwise about the origin, the following are true: 1 For a rotation of 90, (x,y) 2 For a rotation of 180, (x,y) 3 For a rotation of 270, (x,y) 13 Glide Reflection: 14 Definition of composition of transformations: 15 omposition Theorem:

5 page 5 of 8 16 Four Isometries:,,, number of reflections: 17 Line Symmetry: 18 Rotational Symmetry: 19 enter of Symmetry: 20 Dilation: Know how to tell if a dilation is a reduction or an enlargement HPTER 10 1 Definition of circle: 2 Vocabulary of a circle: center, radius, chord, diameter (know what these are and how to identify them) 3 Secant: 4 Tangent: 5 Tangent ircles: 6 oncentric circles: 7 Theorem 101: 8 Theorem 102: S 9 entral ngle, minor arc, major arc, semicircle: (know the vocab and the notation) 10 Measure of a Minor rc: 11 Measure of a Major rc: 12 rc ddition Postulate: 13 ongruent ircles and congruent arcs: Know how to identify them

6 page 6 of 8 14 Theorem 103: If then 15 isecting rcs: If then Y T 16 Theorem 104: If then 17 Theorem 105: If then G 18 Theorem 106: D if and only if D 19 Inscribed ngle and Intercepted rc: Know the vocabulary and how to recognize them in a picture 20 Measure of an Inscribed Theorem 108: Theorem 109: Theorem 1010: ngle Theorem: m D = m D = m = quadrilateral can be inscribed in a circle if and only if its Theorem 1011: Theorem 1012: Theorem 1013: ngles Inside the ngles Outside the ircle Theorem: ircle Theorem: W Y m 1 = m 1 = m 1 = m 2 = m 3 = m 2 = m 2 =

7 page 7 of 8 21 Inscribed Polygon and the circumscribed circle: 22 Segments of hords Theorem: Segments of Secants Theorem: Segments of Secants and Tangents Theorem: (x, y) 23 Standard Equation of a ircle: enter: Radius: HPTER Formulas: rea Perimeter Square Rectangle Parallelogram Triangle dd up all the sides Trapezoid dd up all the sides Rhombus dd up all the sides Kite dd up all the sides Similar Polygons ircle Sector rea of a sector rc Length: M Regular polygon N Know how to measure height

8 page 8 of 8 2 rea ongruence Postulate and rea ddition Postulate: Know how to apply them 3 Probability of an event: e able to apply 4 Geometric probability: e able to apply 5 Probability and Length: e able to apply 6 Probability and rea: e able to apply HPTER Three-dimensional Shapes: Number of bases (General) Lateral rea Formula (General) Surface rea Formula (General) Volume Formula Not applicable 2 ube Formulas: Lateral rea: Surface rea: Volume: 3 Vocabulary words: Polyhedron, faces, edges, vertex, base(s), lateral faces, base edges, slant height, lateral edges, height 4 Euler s Theorem: 5 ross Section: Know the shapes of different cross-sections to a figure 6 Nets: e able to recognize the net for a figure 7 avalieri s Principle: 8 Great circle of a sphere: 9 Hemisphere: 10 Similar Solids: If the Scale factor of two similar solids is a : b, then orresponding lengths have a scale factor of orresponding perimeters have a scale factor of orresponding areas have a scale factor of orresponding volumes have a scale factor of June 2010