Geometry and Geometry Foundations
Syllabus/Standards
Centura Public School
2011-2012
(Black asterik is Geometry and Blue asterik is
Geometry Foundations)
Chapter One Key Concepts
• Tools of Geometry
Chapter One Lesson Objectives
• Make nets and drawing of three-dimensional figures (12.2.4.a)
• Understand basic terms and postulates
• Find/compare lengths of segments (12.1.2.b, 12.2.5.b, 12.3.3.f,
12.3.3.g, 12.3.3.h)
• Find/compare measures of angles (12.1.2.b, 12.2.5.b, 12.3.3.f,
12.3.3.g, 12.3.3.h)
• Identify special angle pairs and use to find angle measures
(12.3.3.l)
• Make basic constructions (12.2.4.a, 12.3.3.l)
• Use Midpoint and Distance Formulas (12.2.2.b)
• Find perimeter/circumference of basic shapes (12.2.4.b, 12.2.5.b,
12.3.3.o)
• Find area of basic shapes (12.2.4.b, 12.2.5.b, 12.3.3.o)
Chapter Two Key Concepts
• Reasoning and Proofs
Chapter Two Lesson Objectives
• Use inductive reasoning (12.3.3.l)
• Recognize/write conditional statements and their parts
• Write biconditionals and recognize definitions (12.2.1.a,
12.2.1.f, 12.3.3.i)
• Use laws for deductive reasoning (12.2.1.a)
• Connect reasoning in algebra and geometry (12.3.3.a, 12.3.3.f,
12.3.3.g, 12.3.3.h)
• Prove angles congruent (12.2.1.a, 12.3.3.f, 12.3.3.g, 12.3.3.h)
Chapter Three Key Concepts
• Parallel and Perpendicular Lines
Chapter Three Lesson Objectives
• Identify relationships between figures in space (12.2.1.a,
12.2.1.c, 12.2.1.d)
• Identify angles formed by two lines and a transversal (12.2.1.a,
12.2.1.c, 12.2.1.d)
• *Prove theorems about parallel lines (12.2.1.a, 12.2.1.c)
• Use properties of parallel lines to find angle measures
• *Prove lines parallel
• Relate parallel and perpendicular lines (12.2.1.a, 12.2.1.c,
12.2.1.d)
• *Use parallel lines to prove theorems about triangles (12.2.1.c,
12.4.3.e)
• Find measures of angles of triangles (12.2.1.f)
• *Construct parallel and perpendicular lines (12.2.4.a)
• Graph/write linear equations (12.3.1.a, 12.3.1.c, 12.3.1.d,
12.3.1.e, 12.3.1.f)
• Relate slope to parallel and perpendicular lines (12.2.1.d,
12.3.1.a, 12.3.1.c, 12.3.1.d, 12.3.1.e, 12.3.1.f)
Chapter Four Key Concepts
• Congruent Triangles
Chapter Four Lesson Objectives
• Recognize congruent figures and corresponding parts (12.2.1.a,
12.2.1.b)
• Prove triangles congruent using postulates and definitions
(12.2.1.b, 12.2.4.a)
• Use/apply properties of isosceles and equilateral triangles
(12.2.1.a, 12.2.1.d, 12.2.2.d)
• Prove right triangles congruent (12.2.1.b, 12.2.1.c, 12.2.1.d,
12.2.1.e, 12.2.2.d, 12.2.4.a, 12.4.3.e)
• Identify congruent overlapping triangles (12.2.1.b, 12.2.1.d)
Chapter Five Key Concepts
• Relationship within Triangles
Chapter Five Lesson Objectives
• *Use properties of midsegments to solve problems (12.2.1.a,
12.2.1.d, 12.2.5.b)
• *Use/identify properties of perpendicular bisectors and angle
bisectors (12.2.1.a, 12.2.1.c, 12.2.1.d, 12.2.4.a, 12.3.3.l)
• *Identify properties of medians and altitudes of a triangle
(12.2.1.a, 12.2.1.c, 12.2.4.a)
• *Use indirect reasoning to write proofs
• *Use inequalities involving angles and sides of triangles
(12.2.1.a, 12.2.1.c, 12.2.1.d, 12.2.5.b, 12.3.1.g, 12.4.3.e)
• *Apply inequalities in two variables (12.2.1.a, 12.2.1.c, 12.2.5.b,
12.3.1.g)
Chapter Six Key Concepts
• Polygons
• Quadrilaterals
Chapter Six Lesson Objectives
• *Find sum of the measures of interior and exterior angles of
polygons (12.4.3.e)
• *Use relations among sides, angles, and diagonals of
parallelograms (12.2.1.c, 12.2.1.d)
• *Determine /prove whether a quadrilateral is a parallelogram
(12.2.1.b, 12.2.2.d, 12.4.3.e)
• Define/classify/use properties of special types of parallelograms
(12.2.1.d, 12.2.2.d)
• *Verify/use properties of trapezoids and kites (12.2.2.d, 12.2.5.b)
• Classify polygons in the coordinate plane (12.2.2.d)
• Name coordinates of special figures by using properties
(12.2.1.d, 12.2.2.a, 12.2.2.d)
• *Prove theorems using figures in the coordinate plane (12.2.2.a)
Chapter Seven Key Concepts
• Similarity
Chapter Seven Lesson Objectives
• Write ratios and solve proportions (12.2.4.b)
• Identify/apply similar polygons (12.2.1.b, 12.2.2.a, 12.2.5.g)
• Use similarity postulates (12.2.1.b, 12.2.1.c, 12.2.2.a, 12.2.4.a,
12.2.4.b, 12.2.5.b)
• Find/use relationships in similar right triangles (12.2.1.b,
12.2.1.c, 12.2.1.d, 12.2.4.b)
• *Use similarity theorems (12.2.1.c, 12.2.1.d, 12.2.4.b)
Chapter Eight Key Concepts
• Right Triangles
• Trigonometry
Chapter Eight Lesson Objectives
• Use the Pythagorean Theorem and its converse (12.2.1.e,
12.2.2.d, 12.2.4.b)
• Use properties of special right triangles (12.2.1.e, 12.2.2.d,
12.2.4.b)
• *Use sine, cosine, and tangent to determine side lengths and
angle measures (12.2.1.e, 12.2.4.b)
• *Use angles of elevation and depression to solve applications
(12.2.1.e, 12.2.4.b, 12.2.5.b)
• *Describe/solve problems using vectors (12.2.1.e)
Chapter Nine Key Concepts
• Transformations
Chapter Nine Lesson Objectives
• **Identify isometries and find translations images of figures
(12.2.3.a)
• **Find reflection images of figures (12.2.3.a, 12.2.4.a)
• **Draw/identify rotation images of figures (12.2.3.a, 12.2.3.b)
• **Identify types of symmetry (12.2.3.a)
• **Understand dilation images of figures (12.2.3.a, 12.2.3.b,
12.2.5.g)
Chapter Ten Key Concepts
• Area
Chapter Ten Lesson Objectives
• Find area of parallelograms and triangles
• Find area of trapezoids, rhombus, or kites
• Find area of regular polygons
• *Find perimeters/areas of similar polygons (12.2.5.g)
• *Find areas of regular polygons and triangles using
trigonometry
• *Find measures of central angles and arcs (12.2.5.e)
• *Find circumference and arc length (12.2.5.e)
• *Find areas of circles, sectors, and segments of circles
• *Use geometric probability
Chapter Eleven Key Concepts
• Surface Area
• Volume
Chapter Eleven Lesson Objectives
•
•
•
•
•
•
•
Recognize polyhedra and cross sections
*Find surface area of prisms and cylinders (12.2.5.a, 12.2.5.f)
*Find surface area of pyramids and cones (12.2.5.a, 12.2.5.f)
*Find volumes of prisms and cylinders (12.2.5.a, 12.2.5.f)
*Find volumes of pyramids and cones (12.2.5.a, 12.2.5.f)
*Find surface area/volume of spheres (12.2.5.a, 12.2.5.f)
*Find areas and volumes of similar solids (12.2.5.a, 12.2.5.f,
12.2.5.g)
Chapter Twelve Key Concepts
• Circles
Chapter Twelve Lesson Objectives
• **Use properties of a tangent to a circle (12.2.1.g)
• **Use congruent chords, arcs, central angles, and perpendicular
bisectors to chords (12.2.1.g)
• **Find measures of of inscribed angles and angles formed by a
tangent and a chord (12.2.1.g)
• **Find measures of angles formed by chords, secants, and
tangents (12.2.1.g)
• **Find lengths of segments associated with circles (12.2.1.g)
• **Write equations of circles and fine center and radii of circles
(12.2.1.g)
• **Draw and describe a locus (12.2.1.g)