Unit Dates

Topics

Content Standards

Chapter 7

7 days

Transformations

·         Rigid Motions in a Plane

·         Reflections

·         Rotations

·         Translations

22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.

Chapter 1

13 days

Basics of Geometry

·         Pattern and Inductive Reasoning

·         Points, Lines and Planes

·         Segments and Their Measure

·         Angles and Their Measure

·         Segment and Angle Bisectors

·         Angle Pair Relationships

·        Introduction to Perimeter, Circumference and Area

1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.

16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.

8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical and exterior angles.

Chapter 2

12 days

Reasoning and Proof

·         Conditional Statements

·         Definitions and Biconditional Statements

·         Deductive Reasoning

·         Reasoning with Properties From Algebra

·         Proving Statements About Segments

·         Proving Statements About Angles

2.0 Students write geometric proofs, including proofs by contradiction.

3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.

Chapter 3

12 days

Perpendicular and Parallel Lines

·         Lines and Angles

·         Proof and Perpendicular Lines

·         Parallel Lines and Transversal

·         Proving Lines are Parallel

·         Using Properties of Parallel Lines

·         Parallel Lines in the Coordinate Plane

·         Perpendicular Lines in the Coordinate Plane

7.0 Students prove and use theorems, involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.

Unit Dates

Topics

Content Standards

Chapter 4

15 days

Congruent Triangles

·        Triangles and Angles

·        Congruence and Triangles

·        Proving Triangles are Congruent: SSS and SAS

·        Proving Triangles are Congruent:  ASA and AAS

·        Using Congruent Triangles

·        Isosceles, Equilateral and Right Triangles

·        Triangles and Coordinate Proof

4.0 Students prove basic theorems involving congruence and similarity.

5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.

12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.

Chapter 5

13 days

Properties of Triangles

·         Perpendicular and Bisectors

·         Bisectors of a Triangle

·         Medians and Altitudes of a Triangle

·         Midsegment Theorem

·         Inequalities in One Triangle

·         Indirect Proof and Inequalities in Two Triangles

2.0 Students write geometric proofs, including proofs by contradiction.

6.0 Students know and are able to use the triangle inequality theorem.

Chapter 6

15 days

Quadrilaterals

·         Polygons

·         Properties of Parallelograms

·         Proving Quadrilaterals are Parallelograms

·         Rhombuses, Rectangles and Squares

·         Trapezoids and Kites

·         Special Quadrilaterals

·         Areas of Triangles and Quadrilaterals

8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

Chapter 8

13 days

Similarity

·         Ratio and Proportion

·         Problem Solving with Proportions

·         Similar Polygons

·         Similar Triangles

·         Proving Triangles Similar

·         Proportions and Similar Triangles

5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

Unit Dates

Topics

Content Standards

Chapter 9

12 days

Right Angles and Trigonometry

·        Simplifying Radical Expressions

·        Similar Right Triangles

·        The Pythagorean Theorem

·        The Converse of the Pythagorean Theorem

·        Special Right Triangles

·        Trigonometric Ratios

·        Solving Right Triangles

15.0 Students prove the Pythagorean Theorem.

19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.

14.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle.  They also know and are able to use elementary relationships between them.  For example,

tanx = sinx/cosx, sin²x + cos²x =1.

20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30-60-90 triangles and 45-45-90 triangles.

Chapter 10

15 days

Circles

·        Tangents

·        Arcs and Chords

·        Inscribed Angles

·        Other Angles

·        Segments Lengths

·        Equations of Circles

7.0 Students prove and use theorems, involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.

21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

Chapter 11

12 days

Area of Polygons and Circles

·        Angle Measure in Polygons

·        Areas of Regular Polygons

·        Perimeters and Areas of Similar Figure

·        Circumference and Arc Length

·        Areas of Circles and Sectors

8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

Unit Dates

Topics

Content Standards

Chapter 12

12 days

Surface Area and Volume

·        Exploring Solids

·        Surface Area of Prisms and Cylinders

·        Surface area of Pyramids and Cones

·        Volume of Prisms and Cylinders

·        Volume of Pyramids and Cones

·        Surface Area of Volume of Sphere

·        Similar Solids

9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.