# Geometry for Grade 9 and 10

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Teacher: Erica
Customers Who Have Viewed This Course: 1718
\$249.00
\$117.00

#### 0 Introduction 01:00

Welcome to Geometry for 9th Grade!

#### 1 Points, Lines, Rays, and Segments 08:45

This lesson offers definitions and examples of points, lines, rays, and segments, creating the perfect introduction to geometric shapes. This lesson includes handouts to keep and practice questions.

By the end of this lesson, students will be able to:

• Define points, lines, rays, and segments
• Define and understand collinearity
• Understand the relationship between points, lines, rays, and segments
• Be able to calculate the lenth of a line segment

#### 2 Midpoints and Bisectors 11:02

This lesson offers a complete overview of geometric midpoints and bisectors, including definitions, practical applications, and use in proofs. This lesson includes practice problems and a handout.

By the end of this lesson, students will be able to:

• Define segment midpoints and bisectors
• Calculate the midpoint of a segment
• Understand the relationship between midpoints and bisecting lines, rays, and segments

#### 3 Planes and Postulates (QUIZ) 16:43

This lesson will introduce students to geometric planes, including how to define, name, and draw planes. This lesson and Unit 1 will then conclude with an overview of the postulates learned throughout the unit concerning points, lines, and planes. This lesson includes a handout and a short quiz reviewing the information learned in Unit 1.

By the end of this lesson, students will be able to:

• Define, name, and draw planes
• Define 'coplanar' and determine if objects are coplanar
• Explain all postulates relating to points, lines, and planes
• Correctly answer all questions on Unit 1 Quiz

#### 4 Everything Angles (QUIZ) 31:16

This lesson will introduce students to geometric angles, including how to define, draw, and measure angles. This lesson and Unit 2 will cover special angles such as complementary, supplementary, and adjacent angles. Students will learn to use knowledge of special angles to solve geometric problems. This lesson and Unit 2 conclude with a short video quiz reviewing the information contained in this lesson. This lesson includes a handout to keep to help guide students.

By the end of this lesson, students will be able to:

• Define, name, draw, and measure angles
• Define 'complementary', 'supplementary', and 'adjacent' angles
• Use their understanding of special angles to complete geometric problems involving angles
• Correctly answer all questions on Unit 2 Quiz

#### 5 Getting Started with Proofs 16:39

This lesson will introduce students to geometric proofs. Students will understand what a proof is, how to set one up, and eventually, how to solve one. This lesson includes a handout to keep reviewing the information discussed in this lesson. By the end of this lesson, students will be able to:

• Define and set up a proof
• Define a number of properties often used to solve proofs
• Solve proofs using geometric properties

#### 6 Perpendicular Lines (QUIZ) 10:28

This lesson will introduce students to perpendicular lines, beginning with the definition of 'perpendicular' and concluding with the use of perpendicular lines in geometric thinking and solving proofs. This lesson and Unit 3 include a short quiz that combines the material from this unit, integrating knowledge of the properties of perpendicular lines with the steps required to solve proofs.

By the end of this lesson, students will be able to:

• Define and identify perpendicular lines
• Understand the properties of perpendicular lines
• Use their understanding of perpendicular lines to inform their proofs
• Correctly answer all questions on Unit 3 Quiz

#### 7 Parallel Lines 10:54

This lesson will introduce students everything related to parallel lines. Students will learn in this lesson how to define and label parallel lines, while forming a deep understanding of the properties of parallel lines. This lesson will also define transversals and explain their relation to parallel lines. This lesson concludes with an explanation of all of the special pairs of angles created by transversals and parallel lines. Included in this less is a handout covering all of the above information.

By the end of this lesson, students will be able to:

• Define 'parallel' and 'transversal'
• Be able to recognize, label, and understand the properties of parallel and transversal lines
• Define and recognize corresponding angles, alternate interior angles, consecutive interior angles, alternate exterior angles

#### 8 Algebra with Parallel Lines (QUIZ) 09:08

This lesson will combine the world of algebra with the geometric understanding that students have formed of parallel lines. This lesson includes several examples of how to use parallel lines to solve algebraic equations and concludes with a quiz applying this concept.

By the end of this lesson, students will be able to:

• Translate geometric understandings into algebraic equations
• Set up alebraic equations using the information from geometric figures
• Correctly answer all questions on Unit 4 Quiz part 1

#### 9 Proofs with Parallel Lines (QUIZ) 16:26

This lesson will combine students' knowledge of parallel lines with their ability to create and solve geometric proofs. This lesson contains a number of practical examples of using the properties of parallel lines to solve proofs and ends with a short quiz testing students' understanding of Unit 4.

By the end of this lesson, students will be able to:

• Set up a geometric proof
• Use their knowledge of parallel lines to solve a proof step by step
• Correctly answer all questions on Unit 4 Quiz part 2

#### 10 Triangles 11:53

This lesson will introduce students triangles, beginning with the definition and properties of a triangle and concluding ways in which to classify a triangle by its lengths or angles.

By the end of this lesson, students will be able to:

• Define triangles
• Understand the properties of triangles
• Recognize isosceles, equilateral, and scalene triangles based on the lengths of a triangle
• Recognize acute, obtuse, and right triangles based on the angles of a triangle

#### 11 Exterior Angles, Medians, and Congruence 12:28

This lesson will further students' understanding of triangles, introducing them to the Exterior Angle Theorem, the role of medians, and congruency. This lesson includes a handout to help students remember these important definitions and theorems.

By the end of this lesson, students will be able to:

• Define the Exterior Angle Theorem
• Use the Exterior Angle Theorem to solve equations
• Define 'median'
• Understand the properties of a median
• Define 'congruent'
• Recognize and label congruent figures and segments

#### 12 Proving Congruence in Triangles (QUIZ) 25:50

This lesson will introduce students to the many ways to show that two triangles are congruent. This lesson covers all of the related postulates with examples and definitions. This lesson includes a handout for students to keep with the above materials. This handout will be helpful while solving future proofs. This lesson and Unit 5 conclude with a quiz testing students' abilities to solve proofs using the information learned in this unit.

By the end of this lesson, students will be able to:

• Prove that two triangles are congruent using the Side-Side-Side Congruence Postulate, the Side-Angle-Side Congruence Postulate, the Angle-Side-Angle Congruence Postulate, and the Angle-Angle-Side Congruence Theorem
• Understand how to use their knowledge of congruence to draw conclusions about triangles
• Set up and solve geometric proofs with more than one pair of congruent triangles
• Correctly answer all questions on Unit 5 Quiz

#### 13 Exploring Polygons 07:55

This lesson will introduce students to polygons, their properties and definitions. This lesson distinguishes between irregular and regular polygons and the different styles of special polygons. This lesson includes a handout including explanations of all of the above.

By the end of this lesson, students will be able to:

• Define and identify all different kinds of polygons
• Distinguish between regular and irregular polygons
• Understand role of diagonals of a polygo

#### 14 Finding the Sum of Interior Angles (QUIZ) 10:56

This lesson will further students' understanding of polygons, incorporating their knowledge of the different types of special polygons to solve for the sum of the interior angles of several types of polygons. This lesson is particularly hands-on, concluding Unit 6 with a quiz the combines algebra and geometric knowledge of polygons.

By the end of this lesson, students will be able to:

• Solve for the sum of the interior angles of any polygon
• Apply this skill to more complex algebraic equations using geometric figures
• Correctly answer all questions on Unit 6 Quiz

#### 15 Parallelograms 13:21

This lesson will introduce students to parallelograms, including their definition and related theorems. In this lesson, all properties of parallelograms will be proven step by step through proofs.

By the end of this lesson, students will be able to:

• Define and identify parallelograms
• Understand the properties of parallelograms
• Use parallelograms to solve proofs

#### 16 Special Parallelograms 16:50

This lesson will further students' understandings of parallelograms by introducing three special parallelograms, squares, rhombuses, and rectangles. This lesson covers the definitions and theorems associated with these special parallelograms. This lesson includes a handout for students to reference containing all of the above information.

By the end of this lesson, students will be able to:

• Define and identify special parallelograms including squares, rhombuses, and rectangles
• Understand the proofs of properties of these parallelograms

#### 17 Trapezoids (QUIZ) 14:32

This lesson will introduce students to one last parallelogram, trapezoids. This lesson discusses the definition of trapezoids, including the associated theorems. This lesson and Unit 7 conclude with a quiz that tests students' understanding of the properties of different quadrilaterals and their applications in both geometry and algebra.

By the end of this lesson, students will be able to:

• Define and identify trapezoids
• Understand the properties of trapezoids
• Use their understanding of all quadrilaterals to solve geometric proofs and algebraic equations
• Correctly answer all questions on Unit 7 Quiz

#### 18 Similarity (QUIZ) 26:13

This lesson will cover all aspects of object similarity including an overview of ratios and proportions, definitions, related theorems and examples. This lesson includes a handout for students to keep explaining further all of the above. Additionally, this lesson contains a short quiz testing students on all aspects of similarity.

By the end of this lesson, students will be able to:

• Define and identify similar objects
• Understand the role of ratios and proportions in similarity
• Understand the theorems resulting from similarity
• Apply this knowledge to geometric problems
• Successfully complete the Unit 8 Quiz part 1

#### 19 Proving Similarity in Triangles (QUIZ) 13:25

This lesson will continue building upon students' understanding of similarity by teaching them a number of ways to prove that triangles are similar. This lesson covers all three triangle similarity theorems or postulates with indepth explanations and examples. Lesson includes a handout with information about each theorem or postulate and a concluding quiz testing students' knowledge of all of the information covered in Unit 8.

By the end of this lesson, students will be able to:

• Explain the theorems and postulates related to triangle similarity
• Prove that two triangles are similar
• Correctly answer all questions on Unit 8 Quiz part 2

#### 20 Working with Radicals 11:08

This lesson will introduce students to the rules of working with radicals. This will lay an important foundation for students to successfully understand the geometric properties of right triangles, which will be covered in the rest of Unit 9. This lesson will teach students what radicals are, how to simplify radical expressions, and how to perform other transformations with them.

By the end of this lesson, students will be able to:

• Name and explain the three rules of working with radicals
• Apply these rules to radical manipulation

#### 21 Similarity Theorem for Right Triangles 13:32

This lesson will cover an important similarity theorem for triangles. This includes a review of the properties of a right triangle and an explanation of the right angle altitude similarity theorem. This lesson includes a handout with definitions and explanations related to right triangles and this theorem.

By the end of this lesson, students will be able to:

• Define the altitude and hypoteneuse of a right triangle
• Understand and explain the altitude similarity theorem
• Apply these understandings to geometric problems

#### 22 The Pythagorean Theorem 11:37

This lesson will introduce students to one of the most important geometric theorems, The Pythagorean Theorem. In this lesson, students will not only be taught what this theorem is, but taught step-by-step how to prove this theorem and its converse. This lesson includes a handout with the important information from this lesson.

By the end of this lesson, students will be able to:

• Explain what The Pythagorean Theorem is
• Prove that the Pythagorean Theorem is correct
• Prove the converse of the Pythagorean Theorem
• Apply The Pythagorean Theorem to geometric figures and questions

#### 23 Special Right Triangles 10:30

This lesson will introduce students to one of the cornerstones of geometry, special right triangles. This lesson covers the two most often occurring right triangles, 45-45-90 and 30-60-90. In this lesson, students will go through step-by-step the proof of each of the theorems associated with these special triangles. This lesson includes practical examples of each special triangle.

By the end of this lesson, students will be able to:

• Explain the properties of both 45-45-90 and 30-60-90 triangles
• Prove the properties of both 45-45-90 and 30-60-90 triangles
• Apply these properties to geometric figures and questions

#### 24 Right Triangle Review (QUIZ) 12:33

A number of very important concepts related to right triangles were introduced in Unit 9. Rather than introducing additional information, this lesson is dedicated to reviewing the key information from the other lessons in this unit. This lesson includes a long video quiz wherein students have the opportunity to solve step-by-step a number of questions ranging from introductory to complex, all based on information covered in Unit 9. Good luck!

#### 25 Trigonometry 14:50

This lesson will introduce students to the world of trigonometry. This lesson will cover the three main trigonometry functions, sine, cosine, and tangent. This lesson includes an important handout showing clearly the relationship between triangles and the trigonometric functions. This lesson also explains how to find trigonometric ratios using scientific calculators.

By the end of this lesson, students will be able to:

• Explain the three trigonometric functions
• Correctly identify the angle and sides necessary to perform a trigonometric function
• Look at a triangle and identify which trigonometric function is necessary to solve for unknowns
• Utilize their scientific calculator to solve trigonometric equations

#### 26 Law of Sines 09:49

This lesson will build upon students' understanding of the sine function in trigonometry by delving into the Law of Sines. Students will learn in this lesson how to apply the Law of Sines to both general triangles and right triangles. This lesson includes a handout for students to keep clearly explaining the Law of Sines and when to use it.

By the end of this lesson, students will be able to:

• Explain the Law of Sines
• Use the Law of Sines to solve for unknowns both in general triangles and right triangles

#### 27 Applications of Trigonometry (QUIZ) 19:05

This lesson will cement students' understanding of trigonometry by showing the practical application of trigonometry in the real world. In this lesson, students will practice solving a number of different trigonometric equations. The focus of this lesson is an in-depth quiz that covers step-by-step all of the information covered in Unit 10.

By the end of this lesson, students will be able to:

• Recognize the applications of trigonometry in the world around them
• Find and draw the right triangle in a word problem
• Solve both right and general triangle problems using trigonometric functions
• Correctly answer all questions on Unit 10 Quiz

#### 28 Everything Circles 06:55

This lesson will introduce students to everything they will need to know about circles to succeed in this unit. This lesson includes all of the terms and definitions that will be later used. Lesson includes an important handout containing all of these terms and definitions for reference during Unit 11.

By the end of this lesson, students will be able to:

• Define and identify circle, chord, diameter, secant, tangent, concentric, and sphere
• Describe the relationship between these terms

#### 29 All About Tangents 21:24

This lesson will introduce students to everything that they will need to know about tangents to succeed in the rest of Unit 11. This lesson explains what tangents are and then shows step-by-step, theorems demonstrating the properties of tangents. This lesson includes a handout with pertinent information about tangents and related theorems.

By the end of this lesson, students will be able to:

• Define and identify a tangent
• Prove step-by-step that tangents from the same external point are congruent
• Use knowledge of the properties of tangents to solve geometric problem

#### 30 Angles, Arcs, and Chords 21:46

This lesson will delve into angles, arcs, and chords. For each topic, this lesson will explain the term, give examples, and demonstrate how to use its properties to solve problems. This lesson will prove related theorems and solve all problems step-by-step.

By the end of this lesson, students will be able to:

• Define and identify angles, arcs, and chords
• Understand the properties of angles, arcs, and chords
• Prove theorems related to angles, arcs, and chords
• Use the properties of angles, arcs, and chords to solve geometric problems
• Correctly answer all questions on Unit 11 Quiz

#### 31 Circles Review (QUIZ) 15:11

Unit 11 covered a number of topics, touching on all facets and properties of circles. This lesson does not introduce new information, but serves as a long quiz covering all of the information learned in Unit 11. Questions on this quiz will range from introductory to complex and will be answered step-by-step in this video. Good luck!

#### 32 Area: Squares, Rectangles, Parallelograms, and Triangles (QUIZ) 27:42

This lesson will introduce students to what the area of a geometric figure is and how to calculate it. This knowledge will be applied to squares, rectangles, parallelograms, and triangles. This lesson contains a quiz testing students' ability to solve for the area of figures. These questions will range from introductory to complex, involving multiple steps and utilization of trigonometry. Each question will be completed by this instructor step-by-step to ensure complete comprehension.

By the end of this lesson, students will be able to:

• Define the perimeter and area of a polygon
• Name the equation for calculating the area of squares, triangles, rectangles, and parallelograms
• Combine knowledge of geometry, algebra, and trigonometry to solve for the area of various polygons
• Correctly answer all questions on Unit 12 Quiz Part 1

#### 33 Area: Rhombuses and Trapezoids (QUIZ) 23:57

This lesson will continue discussing how to calculate the area of a geometric figure, with a focus on rhombuses and trapezoids. This lesson contains a quiz testing students' ability to solve for the area of rhombuses and trapezoids. These questions will range from introductory to complex, involving multiple steps and utilization of trigonometry. Each question will be completed by this instructor step-by-step to ensure complete comprehension.

By the end of this lesson, students will be able to:

• Explain the equation for calculating the area of rhombuses and trapezoids
• Combine knowledge of geometry, algebra, and trigonometry to solve for the area of these figures
• Correctly answer all questions on Unit 12 Quiz Part 2

#### 34 Area: Circles (QUIZ) 22:50

This lesson will continue exploring the ways to calculate the area of a geometric figure, with a focus on circles and sectors. This lesson contains a quiz testing students' ability to solve for the area of circles and sectors. These questions will range from introductory to complex, involving multiple steps and utilization of trigonometry. Each question will be completed by this instructor step-by-step to ensure complete comprehension.

By the end of this lesson, students will be able to:

• Define a sector and describe its relation to a circle
• Name the equation for calculating the area of circles and sectors
• Combine knowledge of geometry, algebra, and trigonometry to solve for the area of these figures
• Correctly answer all questions on Unit 12 Quiz Part 3

#### 35 Volume: Prisms and Pyramids 08:59

This lesson will introduce students to what the volume of a geometric figure is and how to calculate it. This knowledge will be applied to prisms and pyramids.

By the end of this lesson, students will be able to:

• Define the volume of a polygon
• Name the equation for calculating the volume of prisms and pyramids
• Combine knowledge of geometry, algebra, and trigonometry to solve for the volume of prisms and pyramids

#### 36 Volume: Cylinders, Cones, and Spheres 06:09

This lesson will continue delving into the theme of volume and how to calculate it. This knowledge will be applied to cylinders, cones, and spheres.

By the end of this lesson, students will be able to:

• Name the equation for calculating the volume of cylinders, cones, and spheres
• Combine knowledge of geometry, algebra, and trigonometry to solve for the volume of cylinders, cones, and spheres

#### 37 Volume: A Review (QUIZ) 17:51

Unit 13 discussed the many three-dimensional figures in the world of geometry and how to calculate their volumes. Rather than introduce new material, this lesson plan covers a number of quiz questions. These questions range from introductory to complex, using trigonometry and combining the knowledge covered in all sections of this unit. All quiz questions will be explained slowly, step-by-step. Good luck!

#### 38 Thank You! 00:24

Course Overview

This 9th grade mathematics course that covers a full year of geometric concepts. This course takes a hands-on approach to math; no concept will be introduced without the accompaniment of concrete examples. Video quizzes are included at the end of each unit, testing students' knowledge of all of the material covered. Each question on the quizzes will be answered step-by-step in the video, ensuring that students understand the concepts covered before continuing on to the next unit. Each unit also includes mulitiple practice worksheets with corresponding answer keys and step-by-step video explanations of the  worksheet solutions. Each unit will build upon the previous units, weaving in skills learned to further understanding. Lessons that introduce new definitions or theorems include a handout for students to reference, clearly reiterating the defintions or theorems. By the end of this course, students will have mastered all the concepts and skills necessary for success in 9th grade geometry!

This course includes:

-37 Video Lessons

-37 Worksheet and Exercise Review Videos (I go over each problem step by step and provide the solution)

-14 Video Unit Quizzes

-27 Printable Practice Worksheets

-27 Practice Worksheet Review Videos

-29 Printable Lesson Handouts

Target Audience

This video course is primarily intended for high school students in 9th or 10th grade Geometry or Geometry Honors

This course covers the following concepts:

Unit 1 Geometric Building Blocks
-Points, lines, rays, bisectors, midpoints, and planes

Unit 2 Angles
-How to measure and categorize angles
-How to work with special pairs of angles

Unit 3 Geometric Proofs
-How to conceptualize and create geometric proofs
-Using postulates and theorems

Unit 4 Perpendicular and Parallel Lines
-Definitions and properties of perpendicular and parallel lines

Unit 5 Triangles
-Categorizations and properties of triangles
-Exterior and interior angles of triangles
-Proving congruence in triangles

Unit 6 Polygons
-Identifying different polygons
-Calculating the interior angles and sum or interior angles

-Properties and practical applications of parallelograms, trapezoids, rhombuses, squares, and rectangles

Unit 8 Similarity
-Using geometric theorems to identify similar polygons
-Proving similarity in triangles

Unit 9 Special Triangles and Working with Radicals
-Categorizations and properties of special triangles
-Proving similarity and congruence with triangles
-Special right triangles

Unit 10 Trigonometry
-Introduction to and application of sine, cosine, and tangent
-Applications of trigonometry to triangles

Unit 11 Circles
-Properties and practical applications of circles
-Features of circles including angles, arcs, tangents, secants, radii, diameter

Unit 12 Area
-Calculating the surface area of triangles, quadrilaterals, circles, and other various polygons

Unit 13 Volume
-Calculating the volume of prisms, pyramids, cylinders, cones, and spheres

• Teacher: Erica
• Areas of expertise: Mathematics, Psychology
• Education: M.Ed. Harvard University, B.A. Boston College
• Interests: Cooking, travel, running
• Skills:
• Associations: The Massachusetts Psychological Association, American Psychological Association
• Issues I care about: Special education, community mental health

#### Lesson 37 Practice Worksheet Answers

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