Grade Level: Honors Geometry

Chapter #1: The Tools of Geometry

Key Learning(s): Students will learn the basic geometry terms and there use for continuing geometry.
Unit Essential Question(s): Why is it important to learn the basic geometry terms and concepts before continuing the course?
Concept:
Points, Lines & Planes
(1.1 – 1 day) / Concept:
Segment Measure
(1.2, 1.3 – 3 days) / Concept:
Angle Measure
(1.4 – 2 days)
Lesson EQ’s:
What are the basic terms and their importance to Geometry? / Lesson EQ’s:
How are the lengths of segments used in everyday life? / Lesson EQ’s:
Why do we need to understand and use angles in Geometry?
Vocabulary:
Point, line, plane, collinear, coplanar, space / Vocabulary:
Line segment, segment addition postulate, between, congruent, precision, constructions, midpoint, segment bisector, distance / Vocabulary:
Degree, vertex, ray, opposite ray, angles, sides, interior, exterior, acute angle, obtuse angle, right angle
Standards: / Standards:
M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane
G.2.1.2.1 Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane
CC2.3HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically. / Standards:
M11.B.2.1.1 Measure and/or compare angles in degrees (up to
360) (protractor must be provided or drawn).
Concept:
Angle Pairs
(1.5 – 1 day)
Lesson EQ’s:
How are the pairs of angles classified?
Vocabulary:
Vertical angles, linear angles, adjacent angles, complementary angles, supplementary angles
Standards:
M11.B.2.1.1 Measure and/or compare angles in degrees (up to 360) (protractor must be provided or drawn).

Grade Level: Honors Geometry

Chapter #2: Reasoning and Proofs

Key Learning(s): inductive reasoning, paragraph proofs, two-column algebraic and geometric proofs
Unit Essential Question(s): What strategies can we use to base conclusions in geometry and how are they used?
Concept:
Types of Reasoning
(2.1, 2.3 – 2 days) / Concept:
Paragraph proofs
(supplemental 2.5 – 2 days) / Concept:
Constructing Proofs
(2.6 – 2 days)
Lesson EQ’s:
Why are conjectures and counterexamples essential to inductive reasoning? / Lesson EQ’s:
How can we use paragraphs to explain problems? / Lesson EQ’s:
How are postulates, axioms, and theorems used to show that a statement is valid?
Vocabulary:
conjecture, counterexample,
hypothesis, conclusion / Vocabulary:
Paragraph proof, open ended, explain, support / Vocabulary:
Postulate, axiom, theorem, proof, two-column proof, algebra proofs
Standards: / Standards:
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios. / Standards:
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios.
Concept:
Proving Segment Relationships (2.7- 1 days) / Concept:
Proving Angle Relationships
(2.8 - 1 days)
Lesson EQ’s:
What is the proof of the segment addition postulate? / Lesson EQ’s:
If two congruent angles form a linear pair, then what type of angles are they?
Vocabulary: / Vocabulary:
Standards:
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios. / Standards:
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios.
Concept:
Logic
(2.2 – 1 day) / Concept:
Deductive Reasoning
(2.4 – 1 day)
Lesson EQ’s:
How do you set up a truth table? / Lesson EQ’s:
What is the difference between the Law of Detachment and the Law of Syllogism?
Vocabulary: disjunction, conjunction, truth table, compound statement, negation, truth value, statement / Vocabulary: Deductive Reasoning, Law of Detachment, Law of Syllogism
Standards:
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios. / Standards:
G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios.

Grade Level: Honors Geometry

Chapter #3: Perpendicular and Parallel Lines

Key Learning(s): Students will learn about perpendicular and parallel lines. They will be able to write the equation of a line given certain characteristics.
Unit Essential Question(s): How are points, lines, and planes related?
Concept:
Parallel lines, transversals, and angles
(3.1, 3.2, 3.5 – 4 days) / Concept:
Lines in the coordinate plane
(3.3, 3.4 – 3 days) / Concept:
Perpendicular lines and distance
(3.6 – 2 days)
Lesson EQ’s:
What relationships are created with lines and planes? / Lesson EQ’s:
How do slope and linear equations relate to parallel and perpendicular lines? / Lesson EQ’s:
Why are perpendicular lines important to distance in geometry?
Vocabulary:
Parallel lines and planes, perpendicular lines, skew lines, transversal, consecutive, alternate, corresponding, interior/exterior / Vocabulary:
Slope, rate of change, slope-intercept form, point-slope form / Vocabulary:
Equidistant
Standards:
M11.B.2.1.1 Measure and/or compare angles in degrees (up to 360) (protractor must be provided or drawn).
G.2.2.1.2 Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles
G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures. / Standards:
M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet)
M11.D.3.2.1 Apply the formula for the slope of a line to solve problems (formula given on reference sheet)
M11.D.3.2.2 Given the graph of the line, 2 points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope, standard and/or slope-intercept form
M11.D.3.2.3 Compute the slope and/or y-intercept represented by a linear equation or graph
G 2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations)
CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically. / Standards:
M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet)
G 2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations)
CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.
G.2.1.4.1 Solve or graph systems of equations or systems of inequalities within a problem situation using coordinate geometry.
CC2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.
CC2.2.HS.D.10 Represent, solve and interpret equations/inequalities
and systems of equations/inequalities algebraically and graphically.

Grade Level: Honors Geometry

Chapter #4: Congruent Triangles

Key Learning(s): We will discuss how triangles sides and angles can relate to geometry.
Unit Essential Question(s):
How are the sides and angles of triangles used in geometry?
Concept:
Classifying triangles and angle measures of triangles
(4.1, 4.2 – 2 days) / Concept:
Triangle Congruence
(4.3, 4.4, 4.5, HL – 4 days)
**two column proofs / Concept:
Isosceles Triangle Theorem
(4.6 – 2 days) **two column proofs
Lesson EQ’s:
How can we use sides and angles of triangles to classify them? / Lesson EQ’s:
How can we use the triangle theorems to prove triangles are congruent? / Lesson EQ’s:
What properties of isosceles triangles help us to find unknown measurements?
Vocabulary:
acute, obtuse, right, equilangular, scalene, isosceles, equilateral / Vocabulary:
Congruent triangles, included angle, included side / Vocabulary:
Vertex angle, base angle
Standards:
M11.C.1.2.3 Identify and/or use properties of isosceles and equilateral triangles
G1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects. / Standards:
M11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solids
G1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects. / Standards:
M11.C.1.2.3 Identify and/or use properties of isosceles and equilateral triangles
G.1.2.1.1 Identify and/or use properties of triangles
G1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects.

Grade Level: Honors Geometry

Chapter #5: Relationships in Triangles

Key Learning(s): We will discuss how triangles sides and angles can relate to geometry.
Unit Essential Question(s):
How are the sides and angles of triangles used in geometry?
Concept:
Bisectors, medians and altitudes (5.1 – 1 days) / Concept:
Triangle Inequalities
(5.2,5.4 – 2 days) / Concept:
Indirect Proofs
(5.3 – 2 days)
Lesson EQ’s:
How do we use medians, altitudes and bisectors in triangles? / Lesson EQ’s:
How can inequalities be used in triangles? / Lesson EQ’s:
How does indirect reasoning work?
Vocabulary:
Perpendicular bisector
Median, altitude / Vocabulary:
Triangle Inequality Theorem / Vocabulary:
Proof by contradiction, indirect reasoning, indirect proof
Standards:
M11.C.1.2.1 Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem)
G.1.2.1.1 Identify and/or use properties of triangles
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects. / Standards:
M11.C.1.2.1 Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem)
G.1.2.1.1 Identify and/or use properties of triangles
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects.

Grade Level: Honors Geometry

Chapter #6 and Lesson 1-6: Polygons

Key Learning(s): polygons, parallelograms, rectangle, rhombus, square, trapezoid
Unit Essential Question(s):
How can we apply the properties of polygons to determine certain figures?
Concept:
Basics of Polygons
(1.6, 6.1 – 1 days) / Concept:
Basic Parallelograms
(6.2, 6.3 – 3 days) / Concept:
Rectangles
(6.4 – 1 day)
Lesson EQ’s:
How dose the name of a polygon relate to finding their angle measures? / Lesson EQ’s:
How can the properties of sides and angles of polygons be used to ensure a quadrilateral is a parallelogram? / Lesson EQ’s:
How do the properties of special parallelograms differ?
Vocabulary:
Polygon, diagonal, concave, convex, n-gon, regular polygon, interior angle sum, exterior angle sum / Vocabulary:
parallelogram / Vocabulary:
Rectangle, rhombus, square
Standards:
M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and
G.1.2.1.4 Identify and/or use properties of regular polygons
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects. / Standards:
M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and
G.1.2.1.2 Identify and/or use properties of quadrilaterals
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects. / Standards:
M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and
G.1.2.1.2 Identify and/or use properties of quadrilaterals
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects.
Concept:
Rhombi, Squares, Kites
(6.5 and Kites ext– 2 days) / Concept:
Trapezoids
(6.6 – 2 days)
Lesson EQ’s:
How can we identify a shape on the coordinate plane using the slope and distance formula? / Lesson EQ’s:
How can we use the properties of trapezoids to find missing values?
Vocabulary:
none / Vocabulary:
Trapezoid, Isosceles trapezoid, median
Standards:
M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and
M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane (formula provided on the reference sheet).
M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet)
G.1.2.1.2 Identify and/or use properties of quadrilaterals
G 2.1.2.3: Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a 2-dimensional shape
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects.
CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically. / Standards:
M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and
G.1.2.1.2 Identify and/or use properties of quadrilaterals
G 2.1.2.3: Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a 2-dimensional shape
CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships between two-dimensional and
three-dimensional objects.
CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.

**High School Midterms after this unit**

Grade Level: Honors Geometry

Chapter #7: Proportions and Similarity

Key Learning(s):
Ratios, similar figures, proportions
Unit Essential Question(s):
How can ratios and proportions be used to find similarity in figures?
Concept:
Proportions
(7.1 – 1 days)
* word problems / Concept:
Similar Figures
(7.2,7.3 – 3 days) / Concept:
Proportional Parts
(7.4, 7.5 – 3 days)
Lesson EQ’s:
How can we use proportions to determine missing information? / Lesson EQ’s:
How do we use proportions to determine missing sides or lengths of figures? / Lesson EQ’s:
How can we use proportional relationships of similar figures in order to find other measurements?
Vocabulary:
Proportion, ratio, cross product / Vocabulary:
Similar polygons, scale factor / Vocabulary:
midsegment
Standards:
M11.A.2.1.3 Identify and/or use proportional relationships in problem solving settings
G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids
G.1.3.1.2 Identify and/or use proportional relationships in similar figures
CC2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.
CC2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures. / Standards:
M11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solids
G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids
G.1.3.1.2 Identify and/or use proportional relationships in similar figures
CC2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.
CC2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures. / Standards:
M11.A.2.1.3 Identify and/or use proportional relationships in problem solving settings
M11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solids
G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids
G.1.3.1.2 Identify and/or use proportional relationships in similar figures
CC2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.
CC2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.
CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.

Grade Level: Honors Geometry

Chapter #8: Right Triangles and Trigonometry

Key Learning(s): radicals, geometric mean, right triangles, trigonometry
Unit Essential Question(s): What relationships exist with sides and angles of right triangles?
Concept:
Radicals
(supplemental – 1 days) / Concept:
Geometric Mean
(8.1 – 2 days) / Concept:
Right Triangles
(8.2, 8.3 – 2 days)
Lesson EQ’s:
How can we use square roots in geometry? / Lesson EQ’s:
How do you use the geometric mean to find unknown sides in right triangles? / Lesson EQ’s:
How can we apply the Pythagorean Theorem to solve real world problems?
Vocabulary: radical, rationalized denominator / Vocabulary: geometric mean / Vocabulary: Pythagorean theorem, special right triangles
Standards:
M11.A.1.1.3 Simplify square roots.
A1.1.1.1.2 Simplify square roots
CC(ALg1)2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.
CC(Alg1)2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers.
CC(Alg1)2.1.HS.F.1 Apply and extend the properties of exponents to solve
problems with rational exponents.
CC(Alg1)2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems. / Standards:
M11.C.1.2.1 Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem) / Standards:
M11.C.1.4.1 Find the measure of a side of a right triangle using the Pythagorean Theorem (Pythagorean Theorem included on the reference sheet)
G.2.1.1.1 Use the Pythagorean theorem to write and/or solve problems involving right triangles
CC2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios.
Concept:
Trigonometry
(8.4, 8.5 – 3 days) / Concept:
Law of Sines and Cosines
(8.6, 8.7 – 3 Days)
Lesson EQ’s:
How do fractions contribute to solving problems in right triangles? / Lesson EQ’s:
How can we use the laws to solve for missing measures in non right triangles?
Vocabulary: trigonometry, trig ratio, sine, cosine, tangent, angle of elevation, angle of depression / Vocabulary: Law of Sines, Law of Cosines, Solving a Triangle
Standards:
G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles
CC2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios. / Standards:
G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles
CC2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.
CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate
trigonometric ratios.

Grade Level: Honors Geometry