Download What`s in KnowRe`s Curricula?

What’s in KnowRe’s Curricula? Geometry Curriculum Chapter 1. Basics of Geometry Lesson Topics 1-­‐1 Undefined Terms A. 
B. 
C. 
D. 
E. 
F. 
Points Lines Planes Intersec@ons of Undefined Figures Line Segments Rays 1-­‐2 Segments A. 
B. 
C. 
D. 
Distance Segment Addi@on Postulate Congruent Segments Construc@on: Duplica@ng a Segment 1-­‐3 Distance and Midpoint A.  Pythagorean Theorem to Determine the Hypotenuse Length B.  Distance and the Distance Formula C.  Midpoint and the Midpoint Formula D.  Segment Bisectors E.  Construc@on: Segment Bisector 1-­‐4 Angles A. 
B. 
C. 
D. 
E. 
F. 
G. 
Angle Components Naming Angles Measuring Angles Classifying Angles Angle Addi@on Postulate Congruent Angles Construc@on: Duplica@ng an Angle 1-­‐5 Angle Rela@onships A. 
B. 
C. 
D. 
E. 
F. 
Adjacent Angles Complementary Angles Supplementary Angles Linear Pairs Ver@cal Angles Angle Bisectors 1-­‐6 Perimeter and Area A. 
B. 
C. 
D. 
Perimeter of Square, Rectangle, and Triangle Circumference Area of Square, Rectangle, and Triangle Area of Circle 1
Geometry Chapter 2. Reasoning and Proof 3. Parallel and Perpendicular Lines Lesson Topics 2-­‐1 Condi@onal and Bicondi@onal Statements A. 
B. 
C. 
D. 
E. 
Condi@onal Statements Counterexamples Nega@on Inverse, Converse, and Contraposi@ve Bicondi@onal Statements
2-­‐2 Algebraic Proofs A. 
B. 
C. 
D. 
Proper@es of Equality Distribu@ve Property Simplifying Algebraic Proof 2-­‐3 Introduc@on to Geometric Proof A. 
B. 
C. 
D. 
Proper@es of Segment Congruence Proper@es of Angle Congruence Proving Segments Congruent Proving Angles Congruent
2-­‐4 Proof and Angle Rela@onships A. 
B. 
C. 
D. 
E. 
Postulates and Theorems Right Angle Theorem Ver@cal Angle Theorem Congruent Complements Theorem Congruent Supplements Theorem
3-­‐1 Parallel Lines and Transversals A. 
B. 
C. 
D. 
E. 
F. 
G. 
H. 
I. 
Parallel Lines Skew Lines Parallel Planes Transversals Interior and Exterior Angles Iden@fying Corresponding Angles Iden@fying Alternate Interior Angles Iden@fying Alternate Exterior Angles Iden@fying Consecu@ve Interior Angles 3-­‐2 Parallel Lines and Angle Pairs A. 
B. 
C. 
D. 
Corresponding Angles Postulate Alternate Interior Angles Theorem Alternate Exterior Angles Theorem Consecu@ve Interior Angles Theorem 3-­‐3 Proving Lines Parallel A. 
B. 
C. 
D. 
Converse of Corresponding Angles Postulate Converse of Alternate Interior Angles Theorem Converse of Alternate Exterior Angles Theorem Converse of Consecu@ve Interior Angles Theorem 3-­‐4 Parallel and Perpendicular Lines A. 
B. 
C. 
D. 
Perpendicular Lines Parallel and Perpendicular Line Theorems Perpendicular Bisectors Construc@on: Perpendicular Bisector 3-­‐5 Equa@ons of Lines A.  Slope B.  Slope-­‐Intercept Form C.  Point-­‐Slope Form 3-­‐6 Slopes of Parallel and Perpendicular Lines A.  Lines with Undefined and Zero Slope B.  Slopes of Parallel and Perpendicular Lines C.  Equa@ons of Parallel and Perpendicular Lines 2
Geometry Chapter 4. Congruent Triangles 5. Rela@onships in Triangles Lesson Topics 4-­‐1 Angles of Triangles A.  Triangle-­‐Angle Sum Theorem B.  Interior and Exterior Angles of Triangles C.  Triangle Exterior Angle Theorem 4-­‐2 Classifying Triangles A.  Triangle Nota@on B.  Classifying Triangles by their Angles C.  Classifying Triangles by their Sides 4-­‐3 Proper@es of Isosceles and Equilateral Triangles A.  Components of Isosceles Triangles B.  Proper@es of Isosceles Triangles C.  Proper@es of Equilateral Triangles 4-­‐4 Congruent Figures A. 
B. 
C. 
D. 
E. 
F. 
Congruent Polygons Congruence Statements Using Congruent Polygons to Determine Measures Third Angles Theorem Proving Polygons Congruent Corresponding Parts of Congruent Triangles are Congruent 4-­‐5 Proving Triangle Congruence A. 
B. 
C. 
D. 
E. 
F. 
Side-­‐Side-­‐Side Congruence Postulate Side-­‐Angle-­‐Side Congruence Postulate Angle-­‐Side-­‐Angle Congruence Postulate Angle-­‐Angle-­‐Side Congruence Theorem Hypotenuse-­‐Leg Congruence Theorem Iden@fying the Reason for Triangle Congruence 5-­‐1 Bisectors A. 
B. 
C. 
D. 
E. 
Distance from a Point to a Line Angle Bisector Theorem and its Converse Perpendicular Bisector Theorem and its Converse Construc@on: Angle Bisector Construc@on: Perpendicular Bisector 5-­‐2 Perpendicular and Angle Bisectors in Triangles A. 
B. 
C. 
D. 
E. 
F. 
G. 
H. 
I. 
Perpendicular Bisectors of Triangles Circumcenters Circumscribed Triangles Angle Bisectors of Triangles Incenters Circles Inscribed in Triangles Construc@on: Circumscribing a Triangle Construc@on: Circle Circumscribing an Equilateral Triangle Construc@on: Inscribing a Circle in a Triangle 5-­‐3 Medians and Al@tudes in Triangles A. 
B. 
C. 
D. 
Medians of Triangles Centroids Al@tudes of Triangles Orthocenters 5-­‐4 Angle-­‐Side Rela@onships in Triangles A.  Using Side Lengths to Compare Interior Angle Measures B.  Using Interior Angle Measures to Compare Side Lengths 5-­‐5 Triangle Inequali@es A.  Triangle Inequality Theorem B.  Determining Possible Lengths of a Missing Side in a Triangle 3
Geometry Chapter 6. Polygons and Quadrilaterals Lesson Topics 6-­‐1 Introduc@on to Polygons A. 
B. 
C. 
D. 
E. 
F. 
Determining if Figures are Polygons Naming Polygons Iden@fying Concave and Convex Polygons Proper@es of Regular Polygons Construc@on: Square Inscribed in a Circle Construc@on: Regular Hexagon Inscribed in a Circle 6-­‐2 Angles of Polygons A.  Sum of the Measures of the Interior Angles in Convex Polygons B.  Measure of Each Interior Angle in Regular Convex Polygons C.  Sum of the Measures of the Exterior Angles of Convex Polygons D.  Measure of Each Exterior Angle of Regular Convex Polygons 6-­‐3 Parallelograms A. 
B. 
C. 
D. 
E. 
F. 
6-­‐4 Test for Parallelograms A.  Using Opposite Sides to Prove a Quadrilateral is a Parallelogram B.  Using Opposite Angles to Prove a Quadrilateral is a Parallelogram C.  Using Diagonals to Prove a Quadrilateral is a Parallelogram D.  Using One Pair of Opposite Sides to Prove a Quadrilateral is a Parallelogram E.  Determining if Quadrilaterals are Parallelograms 6-­‐5 Rectangles A. 
B. 
C. 
D. 
Defini@on of Rectangle Proper@es of Diagonals in Rectangles Determining if a Parallelogram is a Rectangle Proper@es of Rectangles 6-­‐6 Rhombuses and Squares A. 
B. 
C. 
D. 
E. 
F. 
G. 
Defini@on of Rhombus Proper@es of Diagonals in Rhombuses Determining if a Parallelogram is a Rhombus Proper@es of Rhombuses Defini@on of Square Determining if a Parallelogram is a Square Proper@es of Squares 6-­‐7 Trapezoids and their Midsegments A. 
B. 
C. 
D. 
E. 
F. 
Defini@on of Trapezoid Components of Trapezoids Defini@on of Isosceles Trapezoid Base Angles of Isosceles Trapezoids Diagonals of Isosceles Trapezoids Midsegments of Trapezoids 6-­‐8 Kites A.  Defini@on of Kite B.  Diagonals of Kites C.  Opposite Angles in Kites Opposite and Consecu@ve Angles and Sides Defini@on of Parallelogram Opposite Sides of Parallelograms Opposite Angles of Parallelograms Diagonals of Parallelograms Proper@es of Parallelograms 4
Geometry Chapter 7. Transforma@ons Lesson Topics 7-­‐1 Transforma@on Nota@on and Transla@ons A.  Transforma@on Nota@on B.  Using Triangle Congruence to Determine if Pairs of Figures are Isometries C.  Iden@fying Transla@ons D.  Determining Preimages and Images E.  Transla@on Func@ons F.  Transla@on Vectors G.  Wri@ng Transla@on Vectors as Transla@on Func@ons 7-­‐2 Reflec@ons A. 
B. 
C. 
D. 
E. 
F. 
G. 
Iden@fying Reflec@ons Iden@fying Lines of Reflec@on Iden@fying Images Reflec@ng in Horizontal and Ver@cal Lines Reflec@ng in the x-­‐axis and y-­‐axis Reflec@ng in y=x and y=-­‐x Determining a Line of Reflec@on 7-­‐3 Symmetry and Rota@ons A. 
B. 
C. 
D. 
E. 
F. 
G. 
Lines of Symmetry Determining if Figures have Rota@onal Symmetry Fold Rota@onal Symmetry Degree of Rota@onal Symmetry Iden@fying Rota@on about a Point Rota@ng a Figure about a Vertex of the Figure Rota@ng about the Origin 7-­‐4 Dila@ons A. 
B. 
C. 
D. 
E. 
Types of Dila@ons Scale Factor Dila@on about a Point Determining if Transforma@ons are Dila@ons Dila@on about the Origin 7-­‐5 Composi@on of Isometries A. 
B. 
C. 
D. 
E. 
F. 
Composi@on Nota@on Composi@on of Reflec@ons in Parallel Lines Composi@on of Reflec@ons in Intersec@ng Lines Glide Reflec@ons Performing Composi@ons of Isometries Iden@fying Composi@ons of Isometries that Map a Preimage onto an Image 5
Geometry Chapter 8. Similar Figures Lesson Topics 8-­‐1 Ra@o and Propor@on A. 
B. 
C. 
D. 
Ra@o Propor@on Equivalent Propor@ons Solving Propor@ons 8-­‐2 Directed Line Segments A.  Ra@os and Segments B.  Using Ra@os of Segments to Determine Segment Length C.  Using Ra@os of Segments to Determine the Coordinates of a Point on a Segment 8-­‐3 Similar Polygons A.  Similarity Statements B.  Using Similarity Statements to Iden@fy Corresponding Parts C.  Propor@onality Statements D.  Scale Factor 8-­‐4 Similar Triangles A. 
B. 
C. 
D. 
E. 
8-­‐5 Propor@ons in Triangles A.  Parallel Lines and Propor@onal Segments B.  Angle Bisectors and Propor@onal Segments 8-­‐6 Midsegments of Triangles A.  Parallel Segments B.  Length Rela@onships Angle-­‐Angle Triangle Similarity Postulate Side-­‐Side-­‐Side Similarity Theorem Side-­‐Angle-­‐Side Similarity Theorem Iden@fying the Reason for a Triangle Similarity Missing Measures in Similar Triangles 6
Geometry Chapter 9. Right Triangles and Trigonometry Lesson Topics 9-­‐1 Right Triangle Similarity A.  Right Triangles and Propor@onality Statements B.  Missing Measures in Similar Right Triangles 9-­‐2 Pythagorean Theorem and Pythagorean Inequali@es A.  Pythagorean Theorem B.  Pythagorean Triples C.  Pythagorean Inequali@es 9-­‐3 Isosceles Right Triangles A.  Determine the Length of the Hypotenuse from a Leg B.  Determine the Length of a Leg from the Hypotenuse 9-­‐4 30°-­‐60°-­‐90° Triangles A.  Determine the Length of the Long Leg and the Hypotenuse from the Short Leg B.  Determine the Length of the Short Leg and the Long Leg from the Hypotenuse C.  Determine the Length of the Short Leg and the Hypotenuse from the Long Leg 9-­‐5 Trigonometric Ra@os A.  Sine, Cosine, and Tangent Ra@os B.  Rela@onship Between the Sine and Cosine Ra@os for Complementary Angles C.  Inverse Trigonometric Ra@os 9-­‐6 Solving Right Triangles A.  Use Trigonometry to Determine Missing Side Lengths in Right Triangles B.  Use Trigonometry to Determine Missing Interior Angles in Right Triangles C.  Define Angle of Eleva@on and Angle of Depression D.  Determine Angle of Eleva@on/Depression E.  Angle of Eleva@on/Depression to Determine Missing Lengths 9-­‐7 Area of Triangles and Law of Sines A.  Area of Triangle using Sine B.  Law of Sines to Determine Measures of Missing Lengths C.  Law of Sines to Determine Measures of Interior Angles in Obtuse Triangles 9-­‐8 Law of Cosines A.  Law of Cosines to Determine Measures of Missing Lengths in Triangles B.  Law of Cosines to Determine Measures of Interior Angles in Triangles 7
Geometry Chapter 10. Circles Lesson Topics 10-­‐1 Introduc@on to Circles A. 
B. 
C. 
D. 
E. 
Center Circle Nota@on Segments in Circles Major and Minor Arcs Central Angles 10-­‐2 Tangents A. 
B. 
C. 
D. 
E. 
F. 
G. 
Tangent Lines Point of Tangency Common Internal and External Tangents Internally and Externally Tangent Circles Concentric Circles Tangent Lines and Radii The Length of Tangent Segments Intersec@ng in the Exterior a Circle 10-­‐3 Inscribed Angles A. 
B. 
C. 
D. 
E. 
F. 
Inscribed Angles and their Intercepted Arcs Inscribed Angles formed by Two Chords Inscribed Angles that Intersect the Same Arc Inscribed Angles formed by a Chord and a Tangent Right Triangles Inscribed in Circles Quadrilaterals Inscribed in Circles 10-­‐4 Special Segment and Angle Rela@onships A.  Measures of Angles formed by Two Chords Intersec@ng in the Interior of a Circle B.  Measures of Angles formed by Secants and/or Tangents Intersec@ng in the Exterior of a Circle C.  Lengths of Segments when Chords Intersect in the Interior of a Circle D.  Lengths of Segments when Two Secants Intersect in the Exterior of a Circle E.  Lengths of Segments when a Secant and a Tangent Intersect in the Exterior of a Circle 10-­‐5 Chord Theorems A.  Congruent Chords and Their Intercepted Arcs B.  Perpendicular Diameters and Chords C.  Chords that are Equidistant from the Center 10-­‐6 Equa@ons of Circles A.  Distance Formula to Derive the Equa@on of a Circle B.  Write an Equa@on of a Circle C.  Determine the Center and the Radius from an Equa@on of a Circle D.  Similar Circles 8
Geometry Chapter Lesson 11. Perimeter, Area, 11-­‐1 Areas of Quadrilaterals and Circumference Topics A. 
B. 
C. 
D. 
Area of Parallelogram Area of Kite Area of Rhombus Area of Trapezoid
11-­‐2 Areas of Triangles A.  Area of Triangle Given Base and Height B.  Deriving the Formula for the Area of Equilateral Triangles C.  Use Side Lengths of Equilateral Triangles to Determine their Area D.  Use Areas of Equilateral Triangles to Determine their Side Lengths
11-­‐3 Perimeter and Area of Regular Polygons A.  Perimeter of Regular Polygons B.  Central Angles and Apothems of Regular Polygons C.  Area of Regular Polygons given Apothem or Perimeter 11-­‐4 Area of Regular Polygons with Right Triangles A.  Area of Regular Polygons Using Special Right Triangles B.  Area of Regular Polygons Using Trigonometry 11-­‐5 Arc Length and Sectors A.  Arc Length B.  Use Arc Length to Determine Measures of Segments and Angles in a Circle C.  Sectors D.  Use Sectors to Determine Measures of Segments and Angles in a Circle 9
Geometry Chapter 12. Solids Lesson 12-­‐1 Introduc@on to Solids Topics A. 
B. 
C. 
D. 
E. 
F. 
G. 
Defining Polyhedra Iden@fying Faces, Ver@ces, Edges Euler's Formula Iden@fying Bases and Lateral Faces Naming Solids Cross Sec@ons of Solids Rota@ons of Two-­‐Dimensional Figures 12-­‐2 Surface Area of Prisms and A. 
Cylinders B. 
C. 
D. 
Nets of Prisms and Cylinders Surface Area of Nets Lateral Area of Right Prisms and Cylinders Surface Area of Right Prisms and Cylinders 12-­‐3 Surface Area of Pyramids and Cones A. 
B. 
C. 
D. 
Nets of Pyramids and Cones Surface Area of Nets Lateral Area of Right Pyramids and Cones Surface Area of Right Pyramids and Cones 12-­‐4 Volume of Prisms and Cylinders A.  Volume of Right Prisms and Cylinders B.  Volume of Oblique Prisms and Cylinders 12-­‐5 Volume of Pyramids and Cones A.  Volume of Right Pyramids and Cones B.  Volume of Oblique Pyramids and Cones
12-­‐6 Surface Area and Volume of Spheres A. 
B. 
C. 
D. 
E. 
12-­‐7 Ra@os of Lengths, Areas, and Volumes of Similar Figures A.  Similar Solids B.  Determine Ra@os of Length, Area, or Volume from a Ra@o of Length C.  Determine a Ra@o of Length from a Ra@o of Area or Volume D.  Determine a Ra@o of Volume from a Ra@o of Area E.  Using a Ra@o of Length and a Measure of Length, Area, or Volume to Determine a Second Measure F.  Using Ra@os of Area or Volume and a Measure of Length to Determine a Measure of Length G.  Using a Ra@o of Area and a Measure of Volume to Determine a Measure of Volume H.  Using a Ra@o of Volume and a Measure of Area to Determine a Measure of Area Segments in Spheres The Great Circle and Hemispheres Surface Area of Spheres Volume of Spheres Surface Area and Volume of Hemispheres
10