GEOMETRY
Unit 1: Points, Lines, Planes, Angles
Essential Question: What are the similarities and differences of spatial properties of points, lines, planes, rays and angles in real world applications to each other?
Chapter: 1
1.1 Building Blocks of Geometry & Using Your Algebra Skills 1: Midpoint-undefined terms, point, line, plane, definition, collinear, coplanar, segment, endpoint, ray, length, congruent segments, bisect, segment bisector, coordinate, distance, between, midpoint, MIDPOINT FORMULA,
1.2 Poolroom Math-intersection, angle, vertex, sides, measure, degrees, congruent angles, protractors, angle bisector
1.3 What’s a Widget?-counterexample, right angle, acute angle, obtuse angle, straight angle, vertical angle, adjacent angles, linear pairs, complementary, supplementary, parallel lines, perpendicular lines, skew lines , postulate, theorem, conjecture
Optional Sections
0.1 Geometric Art 0.2 Line Designs
0.3 Circle Designs 0.4 Op Art
0.5 Knot Designs 0.6 Islamic Tile Designs
1.4 Polygons 1.5 Triangles and Special Quadrilaterals
1.6 Circles 1.7 A Picture is Worth a Thousand Words
1.8 Space Geometry Exploration: Geometric Probability I
1.3 Points, Lines, and Planes-undefined terms, point, line, plane, definition, postulates, collinear, coplanar, endpoints, segment, ray
1.4 Sketching Intersections-intersection
1.5 Segments and Their Measures-coordinate, distance, length, between, congruent segments
1.6 Angles and Their Measures-angle, vertex, sides, measure, degree, congruent angles, acute angle, right angle, obtuse angle, straight angle, protractor
2.1 Segment Bisectors-midpoint, segment bisector, bisect, MIDPOINT FORMULA
2.2 Angle Bisectors-angle bisector, congruent angles
2.3 Complementary and Supplementary Angles-complementary, supplementary, adjacent, theorem
*2.4 Vertical Angles-vertical angles, linear pair (identification only see Unit 2)
3.1 Relationships Between Lines-parallel lines, perpendicular lines, skew lines, conjecture, counterexample
3.2 Theorems About Perpendicular Lines
KCCT: Lesson 11 p 86, lesson 12 p 92, lesson 17 p 122
Ladders to Success: Topic 6 p 130 and 139, Topic 2 p 42
Core Content: 3.1.1 (DOK 2), 3.1.2, 3.1.3. (DOK 2), 3.1.4, 3.3.1 (DOK 2)
Program of Studies: SM5, SM1, SM2, MPA 2, SM 4, SR6
3.1.1 / analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines and planes (e.g., betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, skew). / 23.1.2 / use spatial relationships to prove basic theorems.
3.1.3 / analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding and alternate interior angles) in real-world and mathematical problems. / 2
3.3.1 / apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). / 2
Key: blue is geometry, green is basic geometry, underlined are definitions to add, * is an addition or deletion, CAPITALS ARE FORUMLAS.
GEOMETRY
Unit 2: Inductive/Deductive Reasoning
Essential Question: How do you use inductive and deductive reasoning to form and prove conjectures about geometric properties?
Chapter: 2
2.1 Inductive Reasoning-inductive reasoning, pattern, prediction,
2.2 Deductive Reasoning-deductive reasoning
2.3 Finding the nth Term-function rule
2.4 Mathematical Modeling-mathematical model, triangular numbers, square numbers, rectangular numbers
2.5 Angle Relationships- if-then statement, hypothesis, conclusion, converse
2.6 Special Angles on Parallel Lines-transversal, corresponding angles, alternate interior angles, alternate exterior angles, same-side interior angles
Using Your Algebra Skills 2: Slope-SLOPE FORMULA
Optional Sections
Exploration: The Seven Bridges of Konigsberg
Exploration: Patterns in Fractals
1.1 Finding and Describing Patterns-pattern, prediction
1.2 Inductive Reasoning-inductive reasoning
*More Patterns, Function Rule, Math Models-function rule, math model, square numbers, triangular numbers, rectangular numbers
2.4 Vertical Angles
2.5 If-Then Statements and Deductive Reasoning- if-then statement, hypothesis, conclusion, deductive reasoning
3.3 Angles Formed by Transversals-transversal, corresponding angles, alternate interior angles, alternate exterior angles, same-side interior angles
3.4 Parallel Lines and Transversals
3.5 Showing Lines are Parallel-converse
3.6 Using Perpendicular and Parallel Lines
Skills Review-Slope (p 665)-SLOPE FORMULA
Optional Sections
2.6 Properties of Equality and Congruence
KCCT: Lesson 12 p 92, Lesson 5 p 36, Lesson 17 p 122
Ladders to Success: Topic 6 p 136, Topic 4 p 86
Core Content: 3.1.2, 3.1.4, 1.3.2 (DOK 3), 3.3.1 (DOK 2), 3.1.3, 3.4.1
Program of Studies: SR1, SR2, SR3, SR6, FS3, SR3, SR5
3.1.2 / use spatial relationships to prove basic theorems.1.3.2 / describe and extend arithmetic and geometric sequences;
determine a specific term of a sequence given an explicit formula;
determine an explicit rule for the nth term of an arithmetic sequence and
apply sequences to solve real-world problems. / 3
3.3.1 / apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). / 2
3.1.3 / analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding and alternate interior angles) in real-world and mathematical problems. / 2
3.4.1 / identify definitions, axioms and theorems, explain the necessity for them and give examples of them.
Key: blue is geometry, green is basic geometry, underlined are definitions to add, * is an addition or deletion, CAPITALS ARE FORUMLAS.
GEOMETRY
Unit 3: Triangle Relations
Essential Question: How can you use properties of triangles to solve problems involving missing sides and angles in real world applications?
Chapter: 3, 4
?1.5 Triangles-triangle, equilateral, isosceles, scalene, equiangular, acute, right, obtuse
4.1 Triangle Sum Conjecture
4.2 Properties of Special Triangles-base, legs, base angles, vertex angle
4.3 Triangle Inequalities-exterior angle, interior angle, remote (opposite) interior angle, adjacent interior angle
4.4 Are There Congruence Shortcuts?-SSS, SAS
4.5 Are There Other Congruence Shortcuts?-ASA, AAS (SAA),
*Hypotenuse-Leg-HL
4.6 Corresponding Parts of Congruent Triangles-corresponding parts, congruent figures, CPCTC
4.7 Flowchart Thinking
4.8 Proving Isosceles Triangle Conjectures
Points of Concurrency (incenter, circumcenter, centroid, orthocenter)-incenter, circumcenter, altitude, orthocenter, median, centroid
Optional Sections
3.1 Duplication Segments and Angles
3.2 Constructing Perpendicular Bisectors
3.3 Constructing Perpendiculars to a Line
3.4 Constructing Angle Bisectors
3.5 Constructing Parallel Lines
Using Your Algebra Skills 3: Slopes of Parallel and Perpendicular Lines
3.6 Construction Problems
Exploration: Perspective Drawing
3.7 Constructing Points of Concurrency
3.8 The Centroid
Exploration: The Euler Line
Using Your Algebra Skills 4: Writing Linear Equations
Exploration: Napoleon’s Theorem
4.1 Classifying Triangles-triangle, equilateral, isosceles, scalene, equiangular, acute, right, obtuse
4.2 Angle Measures of Triangles-interior angle, exterior angle, remote (opposite) interior angle, adjacent interior angle
4.3 Isosceles and Equilateral Triangles-legs, base, base angles, vertex angle
4.7 Triangle Inequalities
*4.6 Medians & Other Points of Concurrency (incenter, circumcenter, centroid, orthocenter)-incenter, circumcenter, altitude, orthocenter, median, centroid
5.1 Congruence and Triangles-corresponding parts, congruent figures, CPCTC
5.2 Proving Triangles are Congruent: SSS and SAS-SSS, SAS
5.3 Proving Triangles are Congruent: ASA and AAS-ASA, AAS (SAA)
5.4 Hypotenuse-Leg Congruence: HL-HL
5.5 Using Congruent Triangles
Optional Sections:
Constructions (segments, angles, perpendicular bisectors, perpendiculars to a line, angle bisectors, parallel lines)
5.6 Angle Bisectors and Perpendicular Bisectors
3.1.7 / solve real-world and mathematical problems by applying properties of triangles (e.g., Triangle Sum theorem and Isosceles Triangle theorems). / 23.1.8 / use the properties of triangles to prove basic theorems.
3.1.12 / apply the concepts of congruence and similarity to solve real-world and mathematical problems. / 3
3.1.13 / prove triangles congruent and similar.
3.4.3 / be able to perform constructions such as a line parallel to a given line through a point not on the line, the perpendicular bisector of a line segment and the bisector of an angle.
3.1.3 / analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding and alternate interior angles) in real-world and mathematical problems. / 2
3.1.5 / classify and apply properties of two-dimensional geometric figures (e.g., number of sides, vertices, length of sides, sum of interior and exterior angle measures). / 2
KCCT: Lesson 14 p 104, Lesson 16 p 116, Lesson 19 p 133
Ladders to Success: Topic 1 p 24, Topic 5 p 108, Topic 7 p 152
Core Content: 3.1.7(DOK 2), 3.1.8, 3.1.12(DOK 3), 3.1.13, 3.4.3, 3.1.3 (DOK 2), 3.1.5
Program of Studies: SM 5, MPA 1, SR 4, SR 3, FS 3, SR 13, FS 1
GEOMETRY
Unit 4: Proving Polygon Properties
Essential Question: How can you use properties of polygons, including special quadrilaterals, to classify, solve, and prove geometric concepts?
Chapter: 5
?1.4 Polygons-polygon, side, vertex, diagonal, convex, concave, equilateral polygon, equiangular polygon, regular polygon
?1.5 Triangles and Special Quads
5.1 Polygon Sum Conjecture-interior angle, INTERIOR ANGLE SUM FORMULA,
5.2 Exterior Angles of a Polygon-exterior angle, EQUIANGULAR FORMULAS
5.3 Kite and Trapezoid Properties-kite, vertex angles, non-vertex angles, trapezoid, isosceles trapezoid, bases, base angles, legs, leg angles
5.4 Properties of Midsegments-midsegment of triangle, midsegment of trapezoid
5.5 Properties of Parallelograms-parallelogram
5.6 Properties of Special Parallelograms-rhombus, rectangle, square
Optional Sections
Explorations: Star Polygons
Using Your Algebra Skills 5: Solving Systems of Linear Equations
5.7 Proving Quadrilateral Properties
6.1 Polygons-polygon, side, vertex, diagonal
6.2 Properties of Parallelograms-parallelogram
6.3 Showing Quadrilaterals are Parallelograms
6.4 Rhombuses, Rectangles, and Squares-rhombus, rectangle, square, kite, vertex angles, non-vertex angles
6.5 Trapezoids-trapezoid, base, leg, base angles, leg angles, isosceles trapezoid, midsegment of a triangle, midsegment of a trapezoid
6.6 Reasoning About Special Quadrilaterals
8.1 Classifying Polygons-convex, concave, equilateral polygon, equiangular polygon, regular polygon
8.2 Angles in Polygons-interior angle, exterior angle
*Angles of Equiangular Polygons-EQUIANGULAR FORMULAS
KCCT: Lesson 13 p 98, Lesson 17 p 122, Lesson 34 p 238
Ladders to Success: Topic 4 p 98, Topic 7 p 165, Topic 3 p 64, Topic 6 p 137:
Core Content: 3.1.5(DOK 2), 3.4.1, 3.3.1, 5.3.3
Program of Studies: SM5, MPA 4, SR 7, SR 2, SR 1, FS 3, FS 1, FS 2, CG 8, SR 4, SR 13, FS 4
3.1.5 / classify and apply properties of two-dimensional geometric figures (e.g., number of sides, vertices, length of sides, sum of interior and exterior angle measures). / 23.4.1 / identify definitions, axioms and theorems, explain the necessity for them and give examples of them.
3.3.1 / apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). / 2
5.3.3 / model, solve and graph first degree, two-variable equations and inequalities in real-world and mathematical problems. / 2
Key: blue is geometry, green is basic geometry, underlined are definitions to add, * is an addition or deletion, CAPITALS ARE FORUMLAS.
GEOMETRY
Unit 5: Right Triangles
Essential Question: How can you use properties of right triangles, including the Pythagorean Theorem, to solve real world problems?
Chapter: 9
9.1 The Theorem of Pythagoras-hypotenuse, leg, PYTHAGOREAN THEOREM
9.2 The Converse of the Pythagorean Theorem-pythagorean triples, converse
Using Your Algebra Skills 8:Radical Expressions-radical, radicand
9.3 Two Special Right Triangles- 45-45-90 TRIANGLES, 30-60-90 TRIANGLES
9.4 Story Problems
9.5 Distance in Coordinate Geometry- DISTANCE FORMULA
Optional Sections
Exploration: A Pythagorean Fractal
Exploration: Ladder Climb
9.6 Circles and the Pythagorean Theorem
4.4 The Pythagorean Theorem and the Distance Formula-leg, hypotenuse, PYTHAGOREAN THEOREM, DISTANCE FORMULA, Pythagorean triple
4.5 The Converse of the Pythagorean Theorem-converse
10.1 Simplifying Square Roots-radical, radicand
10.2 45-45-90 Triangles- 45-45-90 TRIANGLES
10.3 30-60-90 Triangles- 30-60-90 TRIANGLES
KCCT: Lesson 10 p 73
Ladders to Success: Topic 5 p 108
Core Content: 2.1.3(DOK 3), 2.1.4, 1.3.1
Program of Studies: SM 5, MPA 1, MPA 6, MPA 7
2.1.3 / apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems. / 32.1.4 / apply special right triangles and the converse of the Pythagorean theorem to solve real-world problems.
1.3.1 / solve real-world and mathematical problems to specified accuracy levels by simplifying expressions with real numbers involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube) and factorials. / 2
Key: blue is geometry, green is basic geometry, underlined are definitions to add, * is an addition or deletion, CAPITALS ARE FORUMLAS.
GEOMETRY
Unit 6: Trigonometry
Essential Question: How can you use trigonometric ratios to find missing lengths and angles of right triangles to solve real world problems?
Chapter: 12
12.1 Trigonometric Ratios-trigonometry, trigonometric ratio, opposite, adjacent, tangent, sine, cosine, solve a right triangle, inverse tangent, inverse sine, inverse cosine
12.2 Problem Solving with Right Triangles-angle of elevation, angle of depression
Optional Sections
12.3 The Law of Sines-LAW OF SINES, TRIANGLE AREA SAS
12.4 The Law of Cosines-PYTHAGOREAN IDENTITY, LAW OF COSINES
12.5 Problem Solving with Trigonometry
Exploration: Indirect Measurement
Exploration: Trigonometric Ratios and the Unit Circle
Exploration: Three Types of Proofs
10.4 Tangent Ratio-trigonometry, trigonometric ratio, opposite, adjacent, tangent
10.5 Sine and Cosine Ratios-sine, cosine
10.6 Solving Right Triangles-solve a right triangle, inverse tangent, inverse sine, inverse cosine, angle of elevation, angle of depression
Optional Sections
*Law of Sines & Law of Cosines-LAW OF SINES, TRIANGLE AREA SAS, PYTHAGOREAN IDENTITY, LAW OF COSINES
KCCT: Lesson 10 p 75
Ladders to Success: Topic 5 p 120-129
Core Content: 2.1.3(DOK 3), 1.3.1
Program of Studies: SM5, MPA 5, MPA 6, MPA 8
2.1.3 / apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems. / 31.3.1 / solve real-world and mathematical problems to specified accuracy levels by simplifying expressions with real numbers involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube) and factorials. / 2
Key: blue is geometry, green is basic geometry, underlined are definitions to add, * is an addition or deletion, CAPITALS ARE FORUMLAS.