Title: Introduction: points, lines and planes
Unit Essential Question(s): Why are points, lines, and planes considered the building blocks of Geometry? How can you describe the attributes of a segment? How can you describe the attributes of an angle?

Key Learning(s): The students must know & use the midpoint and distance formulas.

Concept:
Nets

Concept:
Points, lines, & planes

Concept:
Measuring Segments

Lesson Essential Questions:
Why is it useful to make nets of 3 dimensional figures?

Lesson Essential Questions:
How do you name points, lines, segments, & rays?

Lesson Essential Questions:
How do you find & compare lengths of segments?

Vocabulary:
net

Vocabulary:
Point, line, plane, segment, ray, collinear points, coplanar points, opposite rays, postulate, intersection

Vocabulary:
Distance, midpoint, segment bisector, perpendicular bisector, Segment Addition Postulate

Concept:
Measuring Angles

Concept:
Special Angle Pairs

Concept:
Midpoint & Distance Formulas

Lesson Essential Questions:
How do you find & compare measures of angles?

Lesson Essential Questions:
Why is it helpful to use special angle pairs to find angle measures?

Lesson Essential Questions:
How are averages used to find the midpoint of a segment? Why is the distance formula helpful/

Vocabulary:
Angle, sides, vertex, measure, congruent angles, acute angle, right angle, obtuse angle, straight angle, Angle Addition Postulate

Vocabulary:
Adjacent angles, vertical angles, complementary angles, supplementary angles, linear pair, angle bisector,

Vocabulary:
Distance formula, midpoint formula

Unit Essential Question(s): How can you make a conjecture and prove that it is true?

Key Learning(s): The students must know the converse, inverse, & contrapositive of a conditional statement.

Concept:
Conditional Statements

Concept:
Biconditionals & Definitions

Concept:
Law of Syllogism & Detachment

Lesson Essential Questions:
How are the forms of conditional statements related?

Lesson Essential Questions:
How are biconditionals related to definitions?

Lesson Essential Questions:
How do you use the Law of Syllogism & Law of Detachment to reach a valid conclusion?

Vocabulary:
Conditional, hypothesis, conclusion, negation, converse, inverse, contrapositive, equivalent statements

Vocabulary:
Biconditional

Vocabulary:
Deductive Reasoning, Law of Syllogism, Law of Detachment

Concept:
Proofs in Equations

Concept:
Proving angles congruent

Concept:

Lesson Essential Questions:
How are algebraic properties useful in Geometry?

Lesson Essential Questions:
How do you use angle theorems to solve more complex situations?

Lesson Essential Questions:

Vocabulary:
Reflexive Property, Symmetric Property, Transitive Property, 2 Column Proof

Vocabulary:
Theorem, Paragraph Proof

Vocabulary:

Unit Essential Question(s): How do you prove that 2 lines are parallel? How do you prove that 2 lines are perpendicular?

Key Learning(s): Students will be able to explain the relationships between various angles formed by parallel lines & a transversal.

Concept:
Lines & Angles

Concept:
Properties of Parallel Lines

Concept:
Proving Lines Parallel

Lesson Essential Questions:
What is true about lines & planes that do not intersect?

Lesson Essential Questions:
What is different about the angle pairs that form when a transversal intersects parallel lines?

Lesson Essential Questions:
How do you prove 2 lines are parallel?

Vocabulary:
Parallel lines, skew lines, parallel planes, transversal, alternate interior angles, consecutive (same side) interior angles, corresponding angles, alternate interior angles

Vocabulary:
alternate interior angles, consecutive (same side) interior angles, corresponding angles, alternate interior angles

Vocabulary:
alternate interior angles, consecutive (same side) interior angles, corresponding angles, alternate interior angles

Concept:
Parallel & Perpendicular Lines

Concept:
Parallel Lines & Triangles

Concept:

Lesson Essential Questions:
How are parallel & perpendicular lines related?

Lesson Essential Questions:
What relationships exist between the interior & exterior angles of triangles?

Lesson Essential Questions:

Vocabulary:

Vocabulary:
Exterior angle of a polygon, remote interior angles

Vocabulary:

Title: Congruent Triangles
Unit Essential Question(s): How do you identify corresponding parts of congruent triangles? How do you show that two triangles are congruent? How can you tell whether a triangle is isosceles or equilateral?

Key Learning(s): Write a full statement of what is essential for students to know and do, representing the most important ideas key to understanding the content.

Concept:
Congruent Figures

Concept:
SSS & SAS
ASA & AAS

Concept:
CPCTC

Lesson Essential Questions:
How do you write a congruence statement?

Lesson Essential Questions:
Are there ways to prove triangles congruent without knowing all the of the pieces?

Lesson Essential Questions:
How do you use CPCTC?

Vocabulary:
Congruent Polygons

Vocabulary:
Included Angle, Included Side

Vocabulary:

Concept:
Isosceles & Equilateral Triangles

Concept:
HL Theorem

Concept:
Congruence in Overlapping Triangles

Lesson Essential Questions:
What are the properties of Isosceles & equilateral triangles?

Lesson Essential Questions:
How is right triangle congruence different from other types of triangle congruence?

Lesson Essential Questions:
How do you identify congruence in overlapping triangles?

Vocabulary:
Base, legs, vertex angle, base angles

Vocabulary:
Hypotenuse, legs

Vocabulary:

Concept:
Inequalities in 1 Triangle

Concept:
Inequalities in 2 Triangles

Concept:

Lesson Essential Questions:
Why are inequalities useful when examining the sides and angles of a triangle?

Lesson Essential Questions:
How can you compare 2 triangles that have 2 pairs of congruent sides?

Lesson Essential Questions:

Vocabulary:

Vocabulary:

Vocabulary:

Title: Polygons and Quadrilaterals
Unit Essential Question(s): How can you find the sum of the measures of the angles of a polygon? How can you classify quadrilaterals? How are sides & angles useful in determining specials case quadrilaterals?

Key Learning(s): Students will be able to explain the relationships between various angles formed by parallel lines & a transversal.

Concept:
Interior & Exterior Angles of Polygons

Concept:
Properties of Parallelograms

Concept:
Proving Parallelograms

Lesson Essential Questions:
How do you find the sum of the measures of the interior & exterior angles of a polygon?

Lesson Essential Questions:
What do you know about the sides & angles of a parallelogram?

Lesson Essential Questions:How do you can you know that a quadrilateral is a parallelogram?

Vocabulary:
Equilateral polygon, equiangular polygon, regular polygon

Vocabulary:
Parallelogram, Opposite Sides, Opposite Angles, Consecutive Angles, Diagonals

Vocabulary:

Concept:
Rhombuses, Rectangles, & Squares

Concept:
Proving Rhombuses, Rectangles, & Squares

Concept:
Trapezoids & Kites

Lesson Essential Questions:
How are rhombuses, rectangles, & squares related?

Lesson Essential Questions:
What do the diagonals tell you about a parallelogram?

Lesson Essential Questions:
How is a isosceles trapezoid different from a trapezoid?
How are triangles useful in understanding kites?

Vocabulary:
Rhombuse, Rectangle, Square

Vocabulary:

Vocabulary:
Trapezoid, bases, legs, base angles, isosceles trapezoid, midsegment of a trapezoid, kite

Concept:
Polygons in the Coordinate Plane

Concept:
Area of Parallelograms & Triangles

Concept:
Area of Rhombuses, Trapezoids, & Kites

Lesson Essential Questions:
What tools can you use to classify polygons in the coordinate plane?

Lesson Essential Questions:
How are the formulas for the areas of parallelograms & triangles related?

Lesson Essential Questions:
What do you need to know about trapezoids, rhombuses, & kites in order to find their areas?

Vocabulary:

Vocabulary:
Base of a Parallelogram, altitude, height

Vocabulary:
Height of a Trapezoid

Title: Similarity
Unit Essential Question(s): How do you use proportions to find side lengths in similar polygons? How do you show 2 triangles are similar? How do you identify corresponding parts of similar figures?

Key Learning(s): Students will be able to prove that triangles are similar and use the concept of corresponding parts of triangles.

Concept:
Ratios & Proportions

Concept:
Similar Polygons

Concept:
Proving Triangles Similar

Lesson Essential Questions:
Why are ratios & proportions useful?

Lesson Essential Questions:
What are similar polygons?

Lesson Essential Questions:
What are the different ways to prove that 2 triangles are similar?

Vocabulary:
Ratio, extended ratio, proportion,

Vocabulary:
Similar Polygons, Extended Proportions, Scale Factor, Scale

Vocabulary:
Indirect Measurement

Concept:
Similarity in Right Triangles

Concept:
Proportions in Triangles

Concept:
Perimeter & Area of Similar Figures

Lesson Essential Questions:
How is the altitude of a right triangle related to similarity?

Lesson Essential Questions:
What relationships occur when triangles are divided within themselves?

Lesson Essential Questions:
How can you find perimeters & areas of similar polygons?

Vocabulary:

Vocabulary:

Vocabulary:

Title: Right Triangles Subject(s): Geometry Grade(s): 10^{th}
Unit Essential Question(s): How do find a side length or angle measure in a right triangle? How do trigonometric ratios relate to similar right triangles?

Key Learning(s): Students will be able to use properties of special right triangles and basic trig ratios to solve right triangles.

Concept:
Pythagorean Theorem & Converse

Concept:
Special Right Triangles

Concept:
Trigonometry

Lesson Essential Questions:
How can the Converse of the Pythagorean Theorem be used to classify a triangle?

Lesson Essential Questions:
Why would you use the properties of special right triangles?

Lesson Essential Questions:
How do you use trigonometric ratios to find missing angles?

Vocabulary:
Pythagorean Triple

Vocabulary:

Vocabulary:
Trigonometric Ratios, Sine, Cosine, Tangent,

Concept:
Angles of Elevation & Depression

Concept:
Area of Regular Polygons

Concept:
Trigonometry & Area

Lesson Essential Questions:
How do you use angles of elevation & depression to solve problems?

Lesson Essential Questions:
How can you find the area of a regular polygon?

Lesson Essential Questions:
How can you use trigonometry to find the area of regular polygons & triangles?

Vocabulary:
Angle of Elevations, Angle of Depression

Vocabulary:
Radius of a Regular Polygon, Apothem

Vocabulary:

Title: Three Dimensional Shapes  Surface Area and Volume
Unit Essential Question(s): How do you find the surface area and volume of a solid? How do the surface areas and volumes of similar solids compare?

Key Learning(s): Students will be able to describe the effects on volume and/or surface area when the dimensions are changed.

Concept:
Surface Area of Prisms & Cylinders

Concept:
Surface Area of Pyramids & Cones

Concept:
Volumes of Prisms & Cylinders

Lesson Essential Questions:
How do you find the surface area of prisms & cylinders?

Lesson Essential Questions:
How do you find the surface area of pyramids & cones?

Lesson Essential Questions:
How do you find the volume of prisms & cylinders?

Vocabulary:
Prism, bases, lateral faces, altitude, height, right prism, oblique prism, lateral area, surface area, cylinder, right cylinder, oblique cylinder

Vocabulary:
Pyramid, base, lateral faces, vertex, altitude, height, regular pyramid, slant height, lateral area, surface area, cone, right cone

Vocabulary:
Volume

Concept:
V olumes of Pyramids & Cones

Concept:
Surface Area & Volumes of Spheres

Concept:
Areas & Volumes of Similar Solids

Lesson Essential Questions:
How do you find the volume of pyramids & cones?

Lesson Essential Questions:
How do you find the surface area & volume of a sphere?

Lesson Essential Questions:
How are the areas & volumes of similar solids related?

Vocabulary:

Vocabulary:
Sphere, center, radius, diameter, great circle, circumference, hemispheres

Vocabulary:
Similar solids

Title: Circles
Unit Essential Question(s): How can you prove relationships between angles & arcs in a circle? How do you find the equation of a circle in a coordinate plane?

Key Learning(s): Students will be able to use the equation of circles and find the arc length or sector.

Concept:
Circles & Arcs

Concept:
Areas of Circles & Sectors

Concept:
Inscribed Angles

Lesson Essential Questions:
How is the measure of an arc related to its corresponding central angle?

Lesson Essential Questions:
What is the difference between finding the area of circle and a sector of a circle?

Lesson Essential Questions:
What are the characteristics of an inscribed angle?

Vocabulary:
Circle, center, diameter, radius, congruent circles, central angle, semicircle, minor arc, major arc, adjacent arcs, circumference, arc length, congruent arcs

Vocabulary:
Sector of a circle

Vocabulary:
Inscribed angle, intercepted arc

Concept:
Circles in the Coordinate Plane

Concept:

Concept:

Lesson Essential Questions:
What information do you need to write the equation of a circle?

Lesson Essential Questions:

Lesson Essential Questions:

Vocabulary:
Standard form of an equation of a circle

Vocabulary:

Vocabulary:

Title: Transformations and Tesselations
Unit Essential Question(s): How can you change a figure’s position without changing its size & shape? How can you change a figure’s size without changing its shape? How do you recognize symmetry in a figure?

Key Learning(s): Students will be able to apply transformations in a coordinate plane.

Concept:
Translations

Concept:
Reflections

Concept:
Rotations

Lesson Essential Questions:
How do you write the rule for a translation in a coordinate plane?

Lesson Essential Questions:
What is the relationship between the image & preimage of a line of reflection?

Lesson Essential Questions:
How do you draw a rotation of a figure?

Vocabulary:
Transformation, translation, preimage, image, isometry

Vocabulary:
Reflection, line of reflection

Vocabulary:
Rotation, center of rotation, angle of rotation, center of a regular polygon

Concept:
Symmetry

Concept:
Dilations

Concept:
Compositions of Reflections

Lesson Essential Questions:
How can you identify the type of symmetry in a figure?

Lesson Essential Questions:
How can you draw dilation images of a figure?

Lesson Essential Questions:
How can map 2 congruent figures onto each other?

Vocabulary:
Symmetry, line symmetry, reflectional symmetry, line of symmetry, rotational symmetry, point symmetry

Vocabulary:
Dilation, center, scale factor, enlargement, reduction

Vocabulary:
Glide reflection

Concept:
Tessellations

Concept:

Concept:

Lesson Essential Questions:
How can you identify figures that tessellate and the transformations & symmetry in tessellations?

Lesson Essential Questions:

Lesson Essential Questions:

Vocabulary:
Tessellation, glide reflectional symmetry, translational symmetry

Vocabulary:

Vocabulary:
