WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ACCELERATED GEOMETRY (June 2014)

Transcription

1 UNIT: Chapter 1 Essentials of Geometry UNIT : How do we describe and measure geometric figures? Identify Points, Lines, and Planes (1.1) How do you name geometric figures? Undefined Terms Point Line Plane Defined Terms Segment Ray Intersection Defined Terms End Points Collinear Points Coplanar Points Opposite Rays G CC.2.3.HS.A.11 Use Segments and Congruence (1.2) What are congruent segments? Postulate Coordinate Distance Between Congruent Segments Use Midpoint and Distance Formulas (1.3) How do you find the distance and the midpoint between two points in the coordinate plane? Midpoint Segment Bisector Measure and Classify Angles (1.4) How do you identify whether an angle is acute, right, obtuse, or straight? Angle Vertex Vertex of an Angle Measure of an Angle Acute Angle Right Angle Obtuse Angle Straight Angle Sides (of an angle) Congruent Angles Angle Bisector

2 G G Describe Angle Pair Relationships (1.5) How do you identify complementary and supplementary angles? Complementary Angle Supplementary Angle Adjacent Linear Pair Vertical Angles CC.2.3.HS.A.13 Classify Polygons (1.6) How do you classify polygons? Polygon Sides Vertex Convex Concave N gon Equilateral Equiangular Regular

3 UNIT: Chapter 2 Reasoning and Proof UNIT : In what way is geometric reasoning supported? What strategies can we use to draw conclusions in geometry? G Use Inductive Reasoning (2.1) How do you use inductive reasoning in mathematics? Conjecture Inductive Reasoning Counter Example CC.2.3.HS.A.6 CC.2.3.HS.A.8 CC.2.2.HS.C.9 Analyze Conditional Statements (2.2) How do you rewrite a biconditional statement? Hypothesis Conclusion Negation Equivalent Perpendicular Conditional Statement If-Then Form Converse Inverse Contrapositive Biconditional Apply Deductive Reasoning (2.3) How do you construct a logical argument? Deductive Reasoning Law of Detachment Law of Syllogism Use Postulates and Diagrams (2.4) How can you identify postulates illustrated by a diagram? Align Perpendicular to a Plane Reason Using Properties from Algebra (2.5) How do you solve an equation? Addition Property Subtraction Property Multiplication Property Division Property Distributive Property Substitution Property

4 Reflexive Property Symmetric Property Transitive Property G Prove Statements about Segments and Angles (2.6) How do you write a geometric proof? Proof Two-Column Proof Theorem G CC.2.3.HS.A.6 CC.2.3.HS.A.8 CC.2.2.HS.C.9 Prove Angle Pair Relationships (2.7) What is the relationship between vertical angles, between two angles that are supplementary to the same angle, and between two angles that are complementary to the same angle?

5 UNIT: Chapter 3 Parallel and Perpendicular Lines UNIT : What relationships exist between the angles formed by lines intersected by a transversal? G G G CC.2.3.HS.A.6 CC.2.3.HS.A.8 Identify Pairs of Lines and Angles (3.1) What angle pairs are formed by the transversals? Parallel Lines Skew Lines Parallel Planes Transversal Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles CC.2.3.HS.A.9 Use Parallel Lines and Transversals (3.2) How are corresponding angles and alternate interior angles related for two parallel lines and a transversal? Prove Lines are Parallel (3.3) How do you prove lines parallel?

6 G G Find and Use Slopes of Lines (3.4) How do you find the slope of a line given the coordinates of two points on the line? Slope G Write and Graph Equations of Lines (3.5) How do you write an equation of a line? Slope-Intercept Form Standard Form CC.2.3.HS.A.11 Prove Theorems about Perpendicular Lines (3.6) How do you find the distance between a point and a line? Distance from a point to a line

7 UNIT: Chapter 4 Congruent Triangles UNIT : What special properties exist for each type of triangle? How is congruency determined? G G G G CC.2.2.HS.C.9 CC.2.3.HS.A.2 Apply Triangle Sum Properties (4.1) How can you find the measure of the third angle of a triangle if you know the measure of the other two angles? Triangle Scalene Isosceles Equilateral Acute Triangles Right Triangles Obtuse Triangles Equiangular Interior Angles of a Triangle Exterior Angles of a Triangle Corollary CC.2.3.HS.A.5 Apply Congruence and Triangles (4.2) What are congruent figures? Congruent Figures Corresponding Parts CC.2.3.HS.A.6 CC.2.3.HS.A.8 Relate Transformations and Congruence (4.3) How do you identify a rigid motion in the plane? Rigid Motion CC.2.3.HS.A.13 Prove Triangles Congruent by SSS (4.4) How can you use side lengths to prove triangles congruent? Prove Triangles Congruent by SAS and HL (4.5) How can you use two sides and an angle to prove triangles congruent? Legs of a Right Triangles Hypotenuse

8 G G G Prove Triangles Congruent by ASA and AAS (4.6) If a side of one triangle is congruent to a side of another triangle, what information about the angles would allow you to prove the triangles are congruent? Flow Proof CC.2.2.HS.C.9 CC.2.3.HS.A.2 Use Congruent Triangles (4.7) How can you use congruent triangles to prove angles or sides congruent? CC.2.3.HS.A.5 CC.2.3.HS.A.6 CC.2.3.HS.A.8 CC.2.3.HS.A.13 Use Isosceles and Equilateral Triangles (4.8) Perform Congruence Transformations (4.9) How are the sides and angles of a triangle related if there are two or more congruent sides or angles? What transformations create an image congruent to the original figure? Legs of an Isosceles Triangle Vertex Angle Base of an Isosceles Triangle Base Angles Transformation Image Translation Reflection Rotation Congruence Transformation

9 UNIT: Chapter 5 Relationships within Triangles UNIT : What special properties exist within each type of triangle? G G Midsegment Theorem and Coordinate Proof (5.1) How do you write a coordinate proof? Midsegment of a Triangle Coordinate Proof CC.2.3.HS.A.13 Use Perpendicular Bisectors (5.2) How do you find the point of concurrency of the perpendicular bisectors of the sides of a triangle? Equidistant Concurrent Point of Concurrency Perpendicular Bisector Circumcenter Use Angle Bisectors of Triangles (5.3) When can you conclude that a point is on the bisector of an angle? Incenter Use Medians and Altitudes (5.4) How do you find the centroid of a triangle? Altitude of a Triangle Median of a Triangle Centroid Orthocenter Use Inequalities in a Triangle (5.5) How do you find the possible lengths of the third side of a triangle if you know the lengths of two sides? Inequalities in Two Triangles and Indirect Proof (5.6) How do you write an indirect proof? Indirect Proof

10 UNIT: Chapter 6 - Similarity UNIT : How can similarity help us determine values of other figures? G G Use Similar Polygons (6.1) If two figures are similar, how do you find the length of a missing side? Similar Polygons Scale Factor CC.2.3.HS.A.2 CC.2.3.HS.A.5 Relate Transformations and Similarity (6.2) How do you identify a similarity transformation in the plane? Dilation CC.2.3.HS.A.6 Prove Triangles Similar by AA (6.3) How can you show that two triangles are similar? Prove Triangles Similar by SSS and SAS (6.4) How do you prove that two triangles are similar by using the SSS Similarity Theorem? Use Proportionality Theorems (6.5) What proportion can you write if a line is parallel to one side of a triangle? Perform Similarity Transformations (6.6) How do you dilate a figure in the coordinate plane? Center of Dilation Reduction Enlargement

11 UNIT: Chapter 7 Right Triangles and Trigonometry UNIT : What are the different methods that can be used to solve a right triangle? G G G G CC.2.3.HS.A.2 CC.2.3.HS.A.5 CC.2.3.HS.A.6 CC.2.3.HS.A.7 CC.2.2.HS.C.9 Apply the Pythagorean Theorem (7.1) Use the Converse of the Pythagorean (7.2) Use Similar Right Triangles (7.3) Special Right Triangles (7.4) If you know the lengths of two sides of a right triangle, how do you find the length of the third side? How can you use the sides of a triangle to determine if it is right? How can you find the length of the altitude to the hypotenuse of a right triangle? How do you find the lengths of the sides of a triangle and a triangle? Pythagorean Triple Geometric Mean Special Right Triangles Apply the Tangent Ratio (7.5) Apply the Sine and Cosine Ratios (7.6) How can you find a leg of a right triangle when you know the other leg and one acute angle? How can you find the lengths of the sides of a right triangle when you are given the length of the hypotenuse and one acute angle? Trigonometric Ratios Tangent Sine Cosine Angle of Elevation Angle of Depression

12 G G Solve Right Triangles (7.7) In a right triangle, how can you find all the sides and angles of the triangle? Solve a Right Triangle CC.2.3.HS.A.2 CC.2.3.HS.A.7 CC.2.2.HS.C.9

13 UNIT: Chapter 8 - Quadrilaterals UNIT : How can we use the properties of polygons to describe their sides and angles? G G Find Angle Measures in Polygons (8.1) How do you find a missing angle measure in a convex polygon? Diagonal G Use Properties of Parallelograms (8.2) How do you find angle and side measures in a parallelogram? Parallelogram CC.2.3.HS.A.11 CC.2.3.HS.A.13 Show that a Quadrilateral is a Parallelogram (8.3) How can you prove that a quadrilateral is a parallelogram? Properties of Rhombuses, Rectangles, and Squares (8.4) What are the properties of parallelograms that have all sides or all angles congruent? Rhombus Rectangle Square Use Properties of Trapezoids and Kites (8.5) What are the main properties of trapezoids and kites? Trapezoid Bases of a Trapezoid Base Angles of Trapezoid Legs of a Trapezoid Isosceles Trapezoid Kite Midsegment of a Trapezoid Identify Special Quadrilaterals (8.6) How can you identify special quadrilaterals?

14 UNIT: Chapter 9 Properties of Transformations UNIT : How can transformation properties affect figures in geometry? G G CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5 Translate Figures and Use Vectors (9.1) How do you translate a figure using a vector? Image Preimage Isometry Vector Initial Point Terminal Point Horizontal Component Vertical Component Component Form Use Properties of Matrices (9.2) Perform Reflections (9.3) Perform Rotations (9.4) Apply Compositions of Transformations (9.5) How do you use matrix operations to translate a figure? How do you reflect a figure in the line y = x? How do you rotate a figure 90, 180, or 270 about the origin? What is a glide reflection? Matrix Element Dimensions Line of Reflection Reflection Rotation Center of Rotation Angle of Rotation Glide Reflection Composition of Transformations

15 G G CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5 Identify Symmetry (9.6) Identify and Perform Dilations (9.7) When does a figure have a line symmetry? How do you use matrices to draw a dilation? Line Symmetry Line of Symmetry Rotational Symmetry Center of Symmetry Scalar Multiplication

16 UNIT: Chapter 10 Properties of Circles UNIT : What are the relationships between a circle and its arcs, lines, segments, and angles? G , G G CC.2.3.HS.A.8 Use Properties of Tangents (10.1) How can you verify that a segment is tangent to a circle? Circle Center of a Circle Radius Chord Diameter Secant Tangent CC.2.3.HS.A.9 CC.2.3.HS.A.13 Find Arc Measures (10.2) How do you find the measure of an arc of a circle? Central Angle Minor Arc Major Arc Semicircle Measure of a Minor Arc Measure of a Major Arc Congruent Circles Congruent Arcs Apply Properties of Chords (10.3) How can you tell if two chords in a circle are congruent? Use Inscribed Angles and Polygons (10.4) How do you find the measure of an inscribed angle? Inscribed Polygon Circumscribed Circle Inscribed Angle Intercepted Arc

17 G CC.2.3.HS.A.8 Apply Other Angles Relationships in Circles (10.5) How do you find the measure of an angle formed by two chords that intersect inside a circle? CC.2.3.HS.A.9 CC.2.3.HS.A.13 Find Segment Lengths in Circles (10.6) What are some properties of chords, secants, and tangents to a circle? Segment of the Chords Secant Segment External Segment Tangent Segment Write and Graph Equations of Circles (10.7) What do you need to know to write the standard equation of a circle? Standard Equation of a Circle

18 UNIT: Chapter 11 Measurements of Figured and Solids UNIT : How can we relate areas, volumes, circumferences, arc lengths to measurements of figures and solids? G G G Circumference and Arc Length (11.1) Areas of Circles (11.2) How do you find the length of an arc of a circle? How do you find the area of a sector of a circle? Circumference Arc Length Sector of a Circle G G CC.2.3.HS.A.8 CC.2.3.HS.A.9 Areas of Regular Polygons (11.3) Use Geometric Probability (11.4) How do you find the area of a regular polygon? How do you find the probability that a point randomly selected in a region is in a particular part of that region? Center of a Polygon Radius of a Polygon Central Angle of a Regular Polygon Probability Geometric Probability Apothen of a Polygon CC.2.3.HS.A.13 CC.2.3.HS.A.14 CC.2.2.HS.C.1 Explore Solids (11.5) When is a solid a polyhedron? Polyhedron Faces Edges Vertex of a Polyhedron Bases of a Prisms Base of a Pyramid Regular Polyhedron Convex Polyhedron Concave Polyhedron Cross Section Platonic Solids

19 G , G G Volume of Prisms and Cylinders (11.6) Volume of Pyramids and Cones (11.7) How do you find the volume of a right prism or right cylinder? How do you find the volume of a pyramid or cone? Volume G G G Surface Area and Volume of Spheres (11.8) How do you find the volume of a sphere? Sphere Center of a Sphere Radius of a Sphere Chord of a Sphere Hemispheres Great Circle G CC.2.3.HS.A.8 Explore Similar Solids (11.9) If two solids are similar, what is the ratio of their surface areas and what is the ratio of their volumes? Similar Solids CC.2.3.HS.A.9 CC.2.3.HS.A.12 CC.2.3.HS.A.13 CC.2.3.HS.A.14

20 UNIT: Chapter 12 - Probability UNIT : How do we find the probability of a simple and compound event? G G CC.2.4.HS.B.6 CC.2.4.HS.B.7 Find Probabilities and Odds (12.1) How do you find the probability of an event? Outcome Event Sample Space Probability of an Event Theoretical Probability Experimental Probability Odds and Favor Odds Against Find Probabilities Using Permutations (12.2) How do you use the formula for permutations? Factorial Permutation Find Probabilities Using Combinations (12.3) How do you use combinations to count possibilities? Combination Find Probabilities of Disjoint and Overlapping Events (12.4) A problem such as find the probability of getting 0, 1, 2, 3, or 4 red cards when you draw 5 cards can require many computations. How can you simplify the solution? Compound Event Overlapping Events Disjoint Events Mutually Events Find Probabilities of Independent and Dependent Events (12.5) If you draw two cards from a standard deck of 52 cards, is the probability that the second card is red affected by the color of the first card? Independent Events Dependent Events Conditional Probability

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