## Topic outline

### News and Helpful Tools

Instructor: Peter Roed

Phone - (989) 773-9473

Email: Proed@Shepherdschools.net - Preferred

Office location: Odyssey MS/HS

Office Hours: After school Monday through Thursday by appointment.

Questions: Please post questions about the course in the Q&A room under the helpful tools section. If it is a personal matter, please email me. I will typically respond within one business day of receiving your message. (Business days are Monday thru Friday, not including holidays)

### Chapter 1 - Tools of Geometry

Chapter 1 Overview

Students begin their study of geometry by learning to reason inductively. They will use the undeﬁned terms point, line, and plane in postulates about segments, rays, lines, planes, and angles. Students will learn how to measure segments and angles and how to use a compass and straightedge to construct geometric ﬁgures. Finally, they will ﬁnd distance on the coordinate plane algebraically and calculate the circumference, perimeter, and area of geometric ﬁgures.

What You’ll Learn Next

- In this chapter, you will learn how to make plausible conclusions based on patterns you observe.
- You will learn the foundation blocks for the structure of geometry.
- These foundations will provide you with ways to measure segments and angles.
- You will also learn to use constructions and the coordinate plane to represent geometric ﬁgures.

Quizzes: 2Pages: 11Assignments: 11### Chapter 2 - Reasoning and Proof

Chapter 2 Overview

Students will apply postulates from Chapter 1, deductive reasoning, and laws of logic to write paragraph proofs. After learning about conditionals, converses, and biconditionals, students will evaluate logical arguments using the Law of Detachment and the Law of Syllogism. They will use algebraic properties to justify each step in solving algebraic equations. Finally, students will prove several theorems about angles.

Objectives:

- You will learn how to write special types of statements known as conditionals, biconditionals, and deﬁnitions.
- You will use such statements and deductive reasoning to conclude that other statements are true.
- Understanding how deductive reasoning works, you will apply it to form conclusions using algebra.
- You will also use it to study elementary proofs and form your ﬁrst signiﬁcant conclusions about geometric relationships.

Quizzes: 2Pages: 8Assignments: 10### Chapter 3 - Parallel and Perpendicular Lines

Chapter 3 Overview

Students will build on their knowledge of angles to prove and use properties of parallel lines. They will use these properties to prove that the sum of the measures of the angles in a triangle is 180, and to ﬁnd the formula for the sum of the angle measures in a polygon having n sides. Students will learn the relationship that different forms of linear equations have with the slopes of parallel and perpendicular lines. Finally, students will construct parallel and perpendicular lines, and quadrilaterals.

Objectives:

- You will use deductive reasoning to make conclusions about parallel and perpendicular lines.
- You will use parallel lines to learn about angle measures in triangles and other polygons.
- You will also learn ways to think about parallel and perpendicular lines in a coordinate plane.

Quizzes: 2Pages: 10Assignments: 14### Chapter 4 - Congruent Triangles

Chapter 4 Overview

Students will use their knowledge of corresponding parts of congruent polygons to study and apply postulates and theorems related to triangle congruence. These include SSS, SAS, ASA, AAS, HL, and the Isosceles Triangle Theorem. Throughout this chapter, students complete progressively more complex proofs. Their work in Chapter 4 will apply to all subsequent proofs in this course.

Objectives

- You will learn the meaning of congruent polygons.
- You will learn how to prove two triangles congruent by ﬁve different methods.
- By learning how to prove triangles congruent, you will discover properties of an isosceles triangle.
- You will also learn how to draw other conclusions, once two triangles have been proved congruent.

Quizzes: 2Pages: 9Assignments: 11### Chapter 5 - Relationships Within Triangles

Chapter 5 Overview

This chapter will focus on presenting and proving relationships within a triangle that students can, in turn, use to prove relationships within other ﬁgures. Some of the relationships involve midsegments, angle bisectors, perpendicular bisectors, altitudes, medians, and inequalities. Students will learn how to form inverses and contrapositives, which prepares them to prove several theorems indirectly and provides another invaluable technique of proof.

Objectives:

- You will learn about geometric relationships within triangles.
- You will learn about three lines that pass through one point and ﬁnd the four sets of such lines that exist for every triangle.
- You will learn about two other types of statements that are related to a conditional, as well as another type of reasoning—indirect reasoning.
- You will apply indirect reasoning to deduce information about inequalities in triangles.

Quizzes: 2Pages: 8Assignments: 9### Chapter 6 - Quadrilaterals

Chapter 6 Overview

Students apply triangle relationships, algebraic techniques, and methods of proof to the study of quadrilaterals. A thorough study of parallelograms leads to an analysis of special parallelograms (rhombuses, rectangles, squares), trapezoids, and kites. Finally, coordinate proof is introduced and used to prove the Trapezoid Midsegment Theorem.

What You'll Learn Next

- In this chapter, you will learn properties of parallelograms and other special quadrilaterals.
- You will learn properties of quadrilaterals that allow you to classify quadrilaterals.
- You will use these properties to help you place ﬁgures in the coordinate plane.
- You will verify properties of ﬁgures using coordinate techniques.

Quizzes: 2Pages: 8Assignments: 10### Chapter 7 Similarity

In this chapter, students will learn properties of ratios and proportions that are needed to study similarity. They will learn ways to prove triangles similar using the definition of similar polygons. Students will find proportional relationships formed by parallel segments, and by angle bisectors within triangles as well as by altitudes to the hypotenuse in right triangles.

Objectives:

- You will learn that similar polygons are polygons that have the same shape but not necessarily the same size.
- You will learn how to prove triangles similar.
- Through proving triangles similar, you will ﬁnd additional relationships within triangles.
- You will also learn how the perimeters and areas of similar ﬁgures are related.

Quizzes: 2Pages: 8Assignments: 10### Chapter 8 - Right Triangles and Trigonometry

Students use the Pythagorean Theorem to ﬁnd missing side lengths and apply properties of 30°-60°-90° and 45°-45°-90° triangles. The sine, cosine, and tangent trigonometric ratios are developed as applications of right triangle geometry. Students use the ratios to ﬁnd unknown lengths and angle measures in diagrams and real-world scenarios involving angles of elevation, angles of depression, and vectors.

Objectives:- You will learn the Pythagorean Theorem and its converse
- You will use the Pythagorean Theorem to find relationships in special right triangles.
- You will use similar right triangles to define the sine, cosine, and tangent ratios.
- With these ratios, you will solve height and distance problems using angles of elevation and angles of depression.

Quizzes: 2Pages: 8Assignments: 10### Chapter 9 - Transformations

Chapter 9 Overview

In this chapter, students will name and examine transformations on a plane. They will identify and perform reﬂections, translations, and rotations, and then combine them as compositions of transformations and glide reﬂections. They then will apply the Fundamental Theorem of Isometries and the Isometry Classiﬁcation Theorem to symmetry and tessellations. Students also study dilations as non-isometric similarity transformations.

What You'll Learn Next

- In this chapter, you will learn how to use transformations known as reflections, translations, and rotations to create a congruent image of a given shape.
- You will learn to use transformations for relating two given congruent shapes to each other.
- You will learn the effects of applying two transformations, one after the other.
- By learning about transformations, you will understand such terms as symmetry and tessellation.

Quizzes: 2Pages: 8Assignments: 8### Chapter 10 Area

In this chapter, students will use concepts from their study of triangles and quadrilaterals to develop area formulas, ﬁrst for quadrilaterals and then for regular polygons and circles. Special area formulas will be derived for parallelograms, rhombuses, trapezoids, and kites. Students also examine the ratios of the perimeters and of the areas of similar ﬁgures. Finally, students will consider arcs and sectors of circles and apply their areas to geometric probability.

Objectives:

- You will learn how ﬁnding the area of a rectangle can help you ﬁnd the areas of parallelograms and triangles.
- You will learn how to ﬁnd the areas of special quadrilaterals and regular polygons.
- You will learn how perimeters and areas of similar ﬁgures are related.
- You will also learn how to ﬁnd measurements of parts of circles.

Quiz: 1Pages: 8Assignments: 12