CHAPTER ONE NOTES LESSON 1.2, POINTS, LINES, AND PLANES Point ______________________________ Line ______________________________ Plane ______________________________ Collinear ___________________________ Coplanar ___________________________ Symbol for Line ______________________ Symbol for line segment _______________ Symbol for Ray ______________________ Homework: __________________________________________________________________ LESSON 1.3, SEGMENTS AND THEIR MEASURE Segment Addition Postulate Distance Formula 2D Distance Formula 3D Segments that have the same length are called _____________________ and the symbol is ______. Pythagorean Theorem Homework: _____________________________________________________________________ LESSON 1.4, ANGLES AND THEIR MEASURES An ________ consists of two different rays that have the same initial point. The rays are the _______ of the angle. The initial point is the ________ of the angle. Angle Addition Postulate Acute Right Obtuse Straight Two angles are ________________ if they share a common vertex and side, but have no common interior points (they do not overlap). Homework: _____________________________________________________________________ LESSON 1.5, SEGMENT AND ANGLE BISECTORS The ______________ of a segment is the point that divides, or ___________, the segment into two congruent segments. Symbol Midpoint Formula 2D Midpoint Formula 3D An __________________ is a ray that divides an angle into two adjacent angles that are _____________. Homework: _____________________________________________________________________ LESSON 1.6 ANGLE PAIR RELATIONSHIPS Two angles are _________________ if their sides form two pairs of opposite rays. Diagram of Vertical Angles Vertical Angles are always _____________________. Two adjacent angles are a _______________________ if their non- common sides are opposite rays. Diagram of Linear Pair Linear Pairs are always _______________________. Two angles are _______________________ if the sum of their measure is 90 degrees. Two angles are _______________________ if the sum of their measure is 180 degrees. Homework: _____________________________________________________________________ LESSON 1.7, INTRODUCTION TO PERIMETER, CIRCUMFERENCE, AND AREA Perimeter, circumference and area formulas Square Rectangle Triangle Circle Homework: -------------------------------------------------------------------- CHAPTER TWO 2.1 Conditional Statements A conditional statement has two parts, a _________________ and a ________________. When the statement is written in the if-then form, the �if� contains the _____________ & the �then� contains the _______________. When you switch the hypothesis and the conclusion, the new conditional statement is called the _______________________. When you negate the hypothesis and conclusion of a conditional statement, you form the ______________________. When you negate and switch, or switch and negate, you form the _________________. Example Conditional Statement ___________________________________________ Converse ______________________________________________________ Inverse ________________________________________________________ Contrapositive __________________________________________________ 2.2 Biconditional Statements A Biconditional Statement is a statement that contains the phrase �_____________________�. For a Biconditional Statement to be true, the conditional statement and the ____________ must both be true. In other words, you should be able to read the statement correctly ____________ ________________. Example Biconditional Statement ________________________________________. 2.3 Deductive Reasoning Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a ___________________ ___________________. Deductive reasoning is one of the keys to success in Geometry. Law of Detachment. ________________________________________ Example __________________________________________________ Law of Syllogism _____________________________________________ Example _____________________________________________________ It is important to understand the logical argument and to be able to reason logically on the EOC exam. The names of the laws are less important. 2.4 Reasoning with Properties from Algebra This lesson is very important for two reasons. First, it demonstrates that in Algebra I, you used Deductive Reasoning when solving basic algebraic equations. You used facts, definitions, and properties to solve algebraic equations. Second, it uses this previous knowledge to �bridge� you to Geometric Proofs. In other words, we will continue to study of Deductive Reasoning in Geometry. We will end up reusing some of the same properties that you learned and used in Algebra. Addition Property _________________________ Subtraction Property _______________________ Multiplication Property ____________________ Division Property _________________________ Reflexive Property ________________________ Symmetric Property _______________________ Transitive Property _______________________ Substitution Property ______________________ Segment Length and Angle Measure Properties 2.5 Proving Statements about Segments Segment Congruence Properties Example of Two Column Proof 2.6 Proving Statements about Angles Angle Congruence Properties Right Angle Congruence Theorem Congruent Supplements Theorem Congruent Complements Theorem Linear Pair Postulate (critical) Vertical Angle Theorem (critical) -------------------------------------------------------------------- Chapter Three Outline 3.1 Lines and Angles Two lines are parallel lines if they are _____________ and _____________________. Two lines are skew lines if they ________________ and _______________________. Parallel Postulate Perpendicular Postulate *Transversal ___________________________________________________________. *Corresponding, Alternate Exterior, Alternate Interior, Consecutive Interior (Same Side) Lesson 3.2, Proof and Perpendicular Lines *Flow Proof Theorem 3.1 Theorem 3.2 Theorem 3.3 Lessons 3.3 & 3.4 Parallel Lines and Transversals Postulate/Theorems and Converses Corresponding Angles Postulate Alternate Interior Angles Theorem Consecutive Interior Angles Theorem Alternate Exterior Angles Theorem Perpendicular Transversal Theorem Lesson 3.5 Using Properties of Parallel Lines Theorem 3.11 Theorem 3.12 Lesson 3.6 Parallel Lines in the Coordinate Plane Slope Bubble Chart Lesson 3.7 Perpendicular Lines in the Coordinate Plane Slopes of Perpendicular Lines Examples: ----------------------------------------------------------- Chapter 4 Congruent Triangles Lesson 4.1Triangles and Angles Names of Triangles Classified by Sides - ______________, _______________, & ________________. Names of Triangles Classified by Angles - ____________, ______________, & _______________ . Each of the three points joining the sides of a triangle is a ______________. In a triangle, two sides sharing a common vertex are called ____________________. In a right triangle, the sides that form the right angle are the ____________. In a right triangle, the side opposite the right angle is called the _________________. (This is always the longest side of a right triangle) The two congruent sides of an isosceles triangle are called the ______________. The third side is called the __________________. The sum of the interior angles of a triangle is always _________________. The angles that are adjacent to the interior angles are called ________________. The measure of an exterior angle is equal to the sum of the _________________________________________________. The acute angles of a right triangle are __________________________. --------------------------------------------------------------------- ------------------------------- Lesson 4.2, Congruence and Triangles Two geometric figures are ______________ if they have exactly the same _______ & __________. The symbol for congruency is _____________. When two figures are congruent, there is a correspondence between their angles and sides such that ________________________ are congruent and __________________ are congruent. If two angles of one triangle are congruent to two angles of another triangle, then _____________________________________________________. Properties of Congruent Triangles. Reflexsive Symmetric Transitive Lessons 4.3 & 4.4, Proving Triangles are Congruent SSS SAS ASA AAS Lesson 4.5, Using Congruent Triangles Planning the Proof a. Draw a Picture b. Mark it with all given information c. Mark it with any additional information that you can deduce d. Look for SSS, SAS, ASA, or AAS When �Deducing� additional information (the key to your proof), look for: a. Common sides b. Vertical angles c. Parallel lines cut by a transversal Lesson 4.6, Isosceles, Equilateral, and Right Triangles The two adjacent angles of an isosceles triangle are called the _____________________. The angle opposite the base of an isosceles triangle is called the ___________________. If two sides of a triangle are congruent, then the _______________________________. If two angles of a triangle are congruent, then the ______________________________. If a triangle is equilateral, then it is ________________________. If a triangle is equiangular, then it is _______________________. There is one additional way to prove triangles are congruent. If you have a right triangles, and you have congruent hypotenuses and legs, then the triangles are congruent. This is called the _________________________________. This is the special case of ASS that only works for right triangles. CHAPTER FIVE PROPERTIES OF TRIANGLES Lesson 5.1, Perpendiculars and Bisectors Perpendicular Bisector Theorem 5.1, Perpendicular Bisector Theorem Theorem 5.2, Converse of the Perpendicular Bisector Theorem Theorem 5.3, Angle Bisector Theorem Theorem 5.4, Converse of the Angle Bisector Theorem HW ___________________________________________________________________ Lesson 5.2, Bisectors of a Triangle Perpendicular Bisector of a Triangle Concurrent Lines Point of Concurrency Circumcenter of the Triangle Theorem 5.5, Concurrency of Perpendicular Bisectors of a Triangle Angle Bisector of a Triangle Incenter of the Triangle Theorem 5.6, Concurrency of Angle Bisectors of a Triangle HW ____________________________________________________________________ Lesson 5.3, Medians and Altitudes of a Triangle Median of a Triangle Centroid of the Triangle Theorem 5.7 Concurrency of Medians of a Triangle Altitude of a Triangle Orthocenter of the Triangle Theorem 5.8, Concurrency of Altitudes of a Triangle HW ____________________________________________________________________ Lesson 5.4, Midsegment Theorem Midsegment of a Triangle Theorem 5.9, Midsegment Theorem HW ____________________________________________________________________ Lesson 5.5, Inequalities in One Triangle Theorem 5.10 Theorem 5.11 Theorem 5.12, Exterior Angle Inequality Theorem 5.13, Triangle Inequality HW ____________________________________________________________________ Lesson 5.6, Inequalities in Two Triangles Theorem 5.14, Hinge Theorem Theorem 5.15, Converse of the Hinge Theorem HW ___________________________________________________________________ Chapter Six 6.1 Polygons KNOW THESE NAMES Number of sides 3 _____________________ Number of sides 4 _____________________ Number of sides 5 _____________________ Number of sides 6 _____________________ Number of sides 7 _____________________ Number of sides 8 _____________________ Number of sides 9 _____________________ Number of sides 10____________________ Number of sides 12 ____________________ Concave ______________________________ Convex _______________________________ All sides are congruent _____________________ All interior angles are congruent ________________ Equilateral and equiangular ___________________ A segment that joins two nonconsecutive vertices _________________ Sum of the interior angles of a triangle is _______________ Sum of the interior angles of a quadrilateral is ___________ HW ____________________________________________________ 6.2 Properties of Parallelograms A _________________ is a quadrilateral with both pairs of opposite sides parallel. Theorem 6.2 Theorem 6.3 Theorem 6.4 Theorem 6.5 6.3 Proving Quadrilaterals are Parallelograms Theorem 6.6 Theorem 6.7 Theorem 6.8 Theorem 6.9 Theorem 6.10 Summary � Proving Quadrilateral are Parallelograms * * * * * * HW _______________________________________________________ 6.4 Rhombuses, Rectangles, and Squares Venn Diagram Rhombus Rectangle Square Rhombus Co0rollary Rectangle Corollary Square Corollary Theorem 6.11 Theorem 6.12 Theorem 6.13 HW ___________________________________________________ 6.5 Trapezoids and Kites Trapezoid Isosceles Trapezoid Theorem 6.14 Theorem 6.15 Theorem 6.16 Theorem 6.17, Midsegment Theorem for Trapezoids Theorem 6.18 Theorem 6.19 HW ___________________________________________________ 6.6 Special Quadrilaterals Wire Diagram Page 367. HW ______________________________________________________ 6.7 Areas of Triangles and Quadrilaterals Postulate 22 Area of a Square Postulate 23 Area Congruence Postulate 24 Area Addition Theorem 6.20 Area of a Rectangle Theorem 6.21 Area of a Parallelogram Theorem 6.22 Area of a Triangle Theorem 6.23 Area of a Trapezoid Theorem 6.24 Area of a Kite Theorem 6.25 Area of a Rhombus HW ____________________________________________________________ CHAPTER SEVEN � HEAVILY TESTED ON EOC TRANSFORMATIONS 7.1 Rigid Motion in a Plane The original figure is called the ________________. The new figure is called the ___________________. The three basic types of transformations are the ____________, _______________,& _________________. Know the Symbology. ________________________________________. An _______________ is a rigid transformation as opposed to a ___________ which is non rigid. HW ___________________________________________ 7.2 Reflections The _________________ is a transformation that acts like a mirror. The mirror line is called the _________________________. Reflection in the x-axis. (x,y) is mapped to _____________. Reflection in the y-axis. (x,y) is mapped to _____________. Examples: A figure in the plan has a ________________________ if the figure can be mapped onto itself by a reflection in the line. Examples: HW ___________________________________________________ 7.3 Rotation A ___________ is a transformation in which a figure is turned about a fixed point. Fixed point is called the ________________. How far the object rotates is called the _______________________________. Easiest way to do this is to rotate the graph paper and read the coordinates of the new point(s). We are normally rotating about the origin. Examples: A figure has ______________________if the figure can be mapped onto itself by a rotation of 180 degrees or less. Examples: HW ______________________________________________________ 7.4 Translations (Vectors are not on the EOC). A ______________________ is a transformation that slides your object across the graph. Right is plus Left is minus Up is plus Down is minus Examples: HW ______________________________________________________ 7.5 Compositions Compositions are simply a combination of transformations. Examples: HW _______________________________________________________ Appendix 2, page 864 (VERY IMPORTANT) Matrix Dilation � Reduction or Enlargement Adding and Subtracting Matrices Representing a Translation Multiplying Matrices (Recommend you use the Calculator) Reflection Matrices Rotation Matrices HW __________________________________________________________ CHAPTER EIGHT SIMILARITY 8.1, Ratio and Proportion Ratio Proportion Cross Product Property Reciprocal Property HW ______________________________________________________________ 8.2, Problem Solving in Geometry with Proportions Additional Properties of Proportions HW ______________________________________________________________ 8.3, Similar Polygons Similar Polygons Theorem 8.1 HW _____________________________________________________________ 8.4 Similar Triangles Postulate 25, Angle-Angle Similarity Postulate HW ______________________________________________________________ 8.5, Proving Triangles are Similar Theorem 8.2, SSS Similarity Theorem Theorem 8.3, SAS Similarity Theorem HW __________________________________________________________________ 8.6, Proportions and Similar Triangles Theorem 8.4, Triangle Proportionality Theorem Theorem 8.5, Converse of the Triangle Proportionality Theorem Theorem 8.6, Three Parallel Lines Theorem Theorem 8.7, Angle Bisected Theorem HW __________________________________________________________________ 8.7, Dilations Dilation Reduction Enlargement HW __________________________________________________________________ CHAPTER NINE RIGHT TRIANGLES AND TRIGONOMETRY INTRODUCTION Lesson 9.1, Similar Right Triangles Theorem 9.1 Similar Right Triangles Theorems 9.2 & 9.3 Geometric Means HW ___________________________________________________________ Lesson 9.2 & 9.3 Pythagorean Theorem Theorem 9.4 Pythagorean Theorem Pythagorean Triples Theorem 9.5 Converse of the Pythagorean Theorem Theorem 9.6, Pythagorean Inequality Theorem 9.7, Pythagorean Inequality HW ______________________________________________________________ Lesson 9.4, Special Right Triangles Theorem 9.8, 45/45/90 Theorem 9.9, 30/60/90 HW _________________________________________________________________ Lesson 9.5 Trigonometric Ratios Sine Cosine Tangent SOH-CAH-TOA Angle of Elevation/Angle of Depression HW __________________________________________________________________ Lesson 9.6 Solving Right Triangles Sine Inverse Cosine Inverse Tangent Inverse HW ___________________________________________________________________ Note: You will not see Trig again until AFM or Precalculus CHAPTER 10, CIRCLES Lesson 10.1, Tangents to Circle Chord Segment � Secant Line � Tangent Line � Theorem 10.1, Line Tangent to Circle Theorem 10.2, Line Perpendicular to Radius Theorem 10.3, Two Segments that are Tangential HW ________________________________________________ Lesson 10.2, Arcs and Chords Central Angle � Minor Arc � Major Arc � Measure of Minor Arc � Measure of Major Arc � Postulate 26, Arc Addition Postulate - Theorem 10.4, Congruent Minor Arcs - Theorem 10.5, Diameter Perpendicular to Chord - Theorem 10.6, Chord as Perpendicular Bisector � Theorem 10.7, Congruent Chords � HW _________________________________________________ Lesson 10.3, Inscribed Angles Inscribed Angle � Intercepted Arc � Theorem 10.8, Measure of Inscribed Angle � Theorem, 10.9, Same Arc � Inscribed - Circumscribed - Theorem 10.1, Inscribed Right Triangle - Theorem 10.11, Inscribed Quadrilateral � HW ____________________________________________________ Lesson 10.4, Other Angle Relationships in Circles Theorem 10.12, Tangent/Chord � Theorem 10.13, Two Chords � Theorem 10.14, Tan/Sec � Theorem 10.14, Two Tan � Theorem 10.14, Two Sec � HW ________________________________________________________ Lesson 10.5, Segment Lengths in Circles Theorem 10.15, Two Chords � Theorem 10.16, Two Secants � Theorem 10.17, Secant/Tangent � HW ________________________________________________________ Lesson 10.6, Equations of Circles Standard Equation of a Circle HW __________________________________________________________ CHAPTER 11, AREA OF POLYGON AND CIRCLES Lesson 11.1, Angle Measures in Polygons Theorem 11.1, Polygon Interior Angles theorem Corallary to Theorem 11.1 Theorem 11.2, Polygon Exterior Angles Theorem Corallary to Theorem 11.21.2008 HW __________________________________________ Lesson 11.2, Areas of Regular Polygons * Theorem 11.3, Area of an Equilateral Triangle Theorem 11.4, Area of Regular Polygon HW __________________________________________ Lesson 11.3, Perimeters and Areas of Similar Figures Theorem 11.5, Areas of Similar Polygons HW __________________________________________ Lesson 11.4, Circumference and Arc Length Theorem 11.6, Circumference of a Circle - Corollary, Arc Length Corollary - HW __________________________________________ Lesson 11.5, Areas of Circles and Sectors Theorem 11.7, Area of a Circle Theorem 11.8, Area of a Sector HW __________________________________________ Lesson 11.6, Geometric Probability Geometric Probability Probability and Length Probability and Area HW __________________________________________ CHAPTER 12 SURFACE AREA AND VOLUME Lesson 12.1, Exploring Solids A _______________ is a solid that is bounded by polygons, called _____________. An ________________ of a polyhedron is a line segment formed by the intersection of two faces. A ______________ of a polyhedron is a point where three or more edges meet. Another name for vertex is a ________________. Types of Solids Prism Pyramid Cone Cylinder Sphere A polyhedron is ________________ is all of its faces are congruent regular polygons. The intersection of a plane and a solid is called a ___________ ______________. Platonic solids Tetrahedron Octahedron Dodecahedron Icosahedron Euler�s Theorem HW __________________________________________________________ Lesson 12.2, Surface Area of Prisms and Cylinders A ______________ is a polyhedron with two congruent faces, called ___________, that lie in parallel planes. The other faces, called __________________, are parallelograms formed by connecting the corresponding vertices of the bases. In a __________________, each lateral edge is perpendicular to both bases. Prisms that have lateral edges that are not perpendicular to the bases are _____________. The _______________ of a polyhedron is the sum of the areas of its faces. The _______________ of a polyhedron is the sum of the areas of its lateral faces. Surface Area of a Right Prism Surface Area of a Right Cylinder HW __________________________________________________________ Lesson 12.3, Surface Area of Pyramids and Cones A __________ is a polyhedron in which the base is a polygon and he lateral faces are triangles with a common vertex. A _______________ has a regular polygon for a base and its height meets the bases at its center. Surface Area of a Regular Pyramid Surface Area of a Right Cone HW __________________________________________________________ Lesson 12.4, Volume of Prisms and Cylinders Volume of a Cube Cavalieri�s Principle Volume of a Prism Volume of a Cylinder HW __________________________________________________________ Lesson 12.5, Volume of Pyramids and Cones Volume of a Pyramid Volume of a Cone HW __________________________________________________________ Lesson 12.6, Surface Area and Volume of Spheres Surface Area of a Sphere Volume of a Sphere HW __________________________________________________________ Lesson 12.7, Similar Solids Similar Solids Theorem HW __________________________________________________________ |
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