I’m having trouble with Chapter 5, Lesson 1, Problem 29.
I have worked the problem, I know what the answer should be, but given the figure, I don’t understand how that could be false.
Without the figure, I understand it.

Answer:

You can never assume anything. You only know what you are given in the definition. Don’t trust the figure. If it doesn’t tell you, you don’t know it. So for problem # 29 we know the following:

It’s a line
AB is less than BC
BC is less than CD
CD is less than DE

While the lengths in the figure look similar (or even equal), we don’t know that they really are similar or equal. Don’t trust anything but the defined statements in the problem and marked items in a figure.

Here is the question to think about. Given the definitions AB < BC < …. can you draw the figure such that the last DE is much larger.

Put some numbers in it and think inches.

AB = 1
BC = 2
CD = 3
DE = 500

Does that fit the definition of the problem? (Not the figure – the definition?)

Again – figures are often only ONE example that fits the problem – but they do not show every example.

Similarity
· Ratio and proportion
· Similar figures

Right Triangle Trigonometry
· Pythagorean Theorem
· Proportions
· Tangent, Sine, and Cosine

Surface Area and Volume
· Geometric solids
· Rectangular solids
· Spheres

Circles
· Radius
· Chords
· Tangents

Transformations
· Reflections

Notes for use: One of the keys of geometry is learning deductive reasoning or how to do proofs. This can be a challenge to teach, so getting a teachers manual will really help here. The second main idea of geometry is getting used to thinking in space with shapes and the relationships between them. Lots of figures should be drawn.

Jacobs’ Geometry utilizes a clear, conversational, engaging approach to teach your student the concepts, principles, and application of Geometry through practical, real-life application! Harold Jacobs guides your student through Geometry, enabling them to discover the concepts & their applications for themselves in order to develop an understanding of the principles that goes beyond simple memorization to pass a test.

Dr. Callahan and Harold Jacobs’ unique instructional approach to math help your student:

Develop a true understanding of geometric principles

Interact with concepts using real-world examples, ensuring they’ll know exactly how to apply the material they are learning to real-life and other academic subjects

Be prepared to take their understanding of Geometry concepts outside the math textbook and successfully apply them to higher math courses, sciences, & everyday life

Make concepts their own

Be equipped with an understanding of the foundational mathematical concepts of Geometry—and once a student truly understands the concepts in Geometry, they are prepared for all higher math & sciences!

Engaging, Real-World Instruction

Understanding both the why and how of Geometry is foundational to your student’s success in high school and college. Jacobs’ Geometry provides students with a clear and thorough understanding of why concepts work, as well as how they are applied to solve real-world problems.

A Top Choice for High School Success & College Prep

Jacobs’ Geometry has proven its ability to guide students towards success and is still the choice of top teachers and schools. The unique instructional method within Jacobs’ Geometry ensures your student understands both the why and how of Geometry and establishes a strong foundation for higher math & science courses. If your student is planning for college or a STEM career, Jacobs’ Geometry ensures they are equipped with the tools they need to succeed!

Guide Your Student Through with Video Instruction!

Dr. Callahan’s instructional videos guide your students through Jacobs’ Geometry in a light-hearted, down-to-earth style. As a longtime university professor, homeschool dad, and math teacher for homeschool groups, Dr. Callahan has plenty of experience with what Geometry concepts students need to know, what they find difficult, and knows how to explain both well.

Free Homework Support!

Dr. Callahan’s Instructional videos come with FREE Homework Help email support from AskDrCallahan, making this course an ideal solution for parents and students alike looking to learn geometry while preparing for the ACT, SAT, and future math courses.

Videos

Geometry Teaching Videos: Approximately 7 hours of video instruction following the Jacobs textbook.

Required to take the course you will also need:

Textbook

.Harold Jacobs’ Geometry: Seeing, Doing, Understanding has proven its ability to guide students towards success and is still the choice of top teachers and schools. The unique instructional method within Jacobs’ Geometry ensures your student understands both the why and how of Geometry and establishes a strong foundation for higher math & science courses. If your student is planning for college or a STEM career, Jacobs’ Geometry ensures they are equipped with the tools they need to succeed!

Master’s Books Teacher’s Guide

Geometry Teacher’s Guide by Jacobs: Contains 1) daily schedule with space to record grades, 2) chapter, mid-term, and final tests for student assessment, and 3) answer keys for all tests utilized in the course.

Solutions Manual

Geometry Solutions Manual: Provides answers to problems, explaining and illustrating the process of the equations, as well as identifying the answers for all exercises in the course, including mid-term and final reviews.

AskDrCallahan Teacher’s Guide Video Syllabus

Geometry Teacher’s Guide by AskDrCallahan: Contains a syllabus used by Dr. Callahan which has a week-by-week plan for which videos to watch and specific problems to work. Includes Dr. Callahan’s test grading guide that makes it easier for the teacher to grade and helps the student learn from their mistakes. Do NOT purchase if you have the online video course. This guide is included in your video access.

Drawing Kit

Geometry Drawing Kit: Geometry drawing kit is used for drawing diagrams as required in the textbook. Includes a compass, protractor, ruler, and triangles as needed for the construction problems. The drawing kit will be the one pictures or equivalent.

Scientific Calculator

Scientific Calculator: We typically use a TI-30, but we sometimes substitute with an equivalent such as a Casio. This calculator is allowed on the ACT. It can be used throughout your student’s academic career and at college.

Jacobs’ Geometry utilizes a clear, conversational, engaging approach to teach your student the concepts, principles, and application of Geometry through practical, real-life application! Harold Jacobs guides your student through Geometry, enabling them to discover the concepts & their applications for themselves in order to develop an understanding of the principles that go beyond simple memorization to pass a test.

Dr. Callahan and Harold Jacobs’ unique instructional approach to math help your student:

Develop a true understanding of geometric principles

Interact with concepts using real-world examples, ensuring they’ll know exactly how to apply the material they are learning to real-life and other academic subjects

Be prepared to take their understanding of Geometry concepts outside the math textbook and successfully apply them to higher math courses, sciences, & everyday life

Make concepts their own

Be equipped with an understanding of the foundational mathematical concepts of Geometry—and once a student truly understands the concepts in Geometry, they are prepared for all higher math & sciences!

Engaging, Real-World Instruction

Understanding both the why and how of Geometry is foundational to your student’s success in high school and college. Jacobs’ Geometry provides students with a clear and thorough understanding of why concepts work, as well as how they are applied to solve real-world problems.

A Top Choice for High School Success & College Prep

Jacobs’ Geometry has proven its ability to guide students towards success and is still the choice of top teachers and schools. The unique instructional method within Jacobs’ Geometry ensures your student understands both the why and how of Geometry and establishes a strong foundation for higher math & science courses. If your student is planning for college or a STEM career, Jacobs’ Geometry ensures they are equipped with the tools they need to succeed!

Guide Your Student Through with Video Instruction!

Dr. Callahan’s instructional videos guide your students through Jacobs’ Geometry in a light-hearted, down-to-earth style. As a longtime university professor, homeschool dad, and math teacher for homeschool groups, Dr. Callahan has plenty of experience with what Geometry concepts students need to know, what they find difficult, and knows how to explain both well.

Free Homework Support!

Dr. Callahan’s Instructional videos come with FREE Homework Help email support from AskDrCallahan, making this course an ideal solution for parents and students alike looking to learn geometry while preparing for the ACT, SAT, and future math courses.

Videos

Geometry Teaching Videos: Approximately 7 hours of video instruction following the Jacobs textbook.

Required to take the course you will also need:

Textbook

.Harold Jacobs’ Geometry: Seeing, Doing, Understanding has proven its ability to guide students towards success and is still the choice of top teachers and schools. The unique instructional method within Jacobs’ Geometry ensures your student understands both the why and how of Geometry and establishes a strong foundation for higher math & science courses. If your student is planning for college or a STEM career, Jacobs’ Geometry ensures they are equipped with the tools they need to succeed!

Master’s Books Teacher’s Guide

Geometry Teacher’s Guide by Jacobs: Contains 1) daily schedule with space to record grades, 2) chapter, mid-term, and final tests for student assessment, and 3) answer keys for all tests utilized in the course.

Solutions Manual

Geometry Solutions Manual: Provides answers to problems, explaining and illustrating the process of the equations, as well as identifying the answers for all exercises in the course, including mid-term and final reviews.

AskDrCallahan Teacher’s Guide Video Syllabus

Geometry Teacher’s Guide by AskDrCallahan: Contains a syllabus used by Dr. Callahan which has a week-by-week plan for which videos to watch and specific problems to work on. Includes Dr. Callahan’s test grading guide that makes it easier for the teacher to grade and helps the student learn from their mistakes. Do not purchase separately if you have the online video course. This guide is included in your video access.

Drawing Kit

Geometry Drawing Kit: A geometry drawing kit is used for drawing diagrams as required in the textbook. Includes a compass, protractor, ruler, and triangles as needed for the construction problems. The drawing kit will be the one pictured or equivalent.

Scientific Calculator

Scientific Calculator: We typically use a TI-30, but we sometimes substitute with an equivalent such as a Casio. This calculator is allowed on the ACT. It can be used throughout your student’s academic career and at college.

Jacobs’ best-selling Geometry course has become a highly respected standard for teaching high school math in both top schools nationwide and within the homeschool market. The Geometry Teacher Guide contains tests, solutions to tests, and a daily schedule.

Master’s Books Jacobs’ Teacher’s Guide

Geometry Teacher’s Guide by Jacobs: Contains

Convenient suggested daily schedule—saving you time!

Tests (chapter, mid-term, final exam, & alternate test versions)

Test Solutions

Practical 3-hole punched perforated pages for ease of use

Required to take the course you will also need:

Videos

Geometry Teaching Videos: Approximately 4 hours of video instruction following the Jacobs textbook. Includes FREE homework support!

Textbook

.Harold Jacobs’ Geometry: Seeing, Doing, Understanding has proven its ability to guide students towards success and is still the choice of top teachers and schools. The unique instructional method within Jacobs’ Geometry ensures your student understands both the why and how of Geometry and establishes a strong foundation for higher math & science courses. If your student is planning for college or a STEM career, Jacobs’ Geometry ensures they are equipped with the tools they need to succeed!

Solutions Manual

Geometry Solutions Manual: Provides answers to problems, explaining and illustrating the process of the equations, as well as identifying the answers for all exercises in the course, including mid-term and final reviews.

AskDrCallahan Teacher’s Guide Video Syllabus

Geometry Teacher’s Guide by AskDrCallahan: Contains a syllabus used by Dr. Callahan which has a week-by-week plan for which videos to watch and specific problems to work on. Includes Dr. Callahan’s test grading guide that makes it easier for the teacher to grade and helps the student learn from their mistakes. Do not purchase separately if you have the online video course. This guide is included inside your video access.

Drawing Kit

Geometry Drawing Kit: A geometry drawing kit is used for drawing diagrams as required in the textbook. Includes a compass, protractor, ruler, and triangles as needed for the construction problems. The drawing kit will be the one pictured or equivalent.

Scientific Calculator

Scientific Calculator: We typically use a TI-30, but we sometimes substitute with an equivalent such as a Casio. This calculator is allowed on the ACT. It can be used throughout your student’s academic career and at college.

Question: how do we work the problem on Chapter 14 test #4.

Answer from Harold Jacobs:

Since all 16 white regions are identical, we can find the area of one of them and multiply it by 16.

This figure represents one of the 16 small squares and one of the white regions.

Since the diameter of the large circle in the figure shown on the test page is 4 units, the side of the square of one of the small squares is 1 unit.

We can find the area of region B by finding the area of regions B & C combined (a quarter of a circle) and subtracting the area of region C (a triangle):

> The area of B & C combined is1/4 (pi r squared) or 1/4 (pi 1 squared) = 1/4 pi

> The area of C is1/2 r squared or 1/2 1 squared = 1/2So B = (B + C) – C = 1/4 pi – 1/2 and the total area of the 16 white regions is16(1/4 pi – 1/2) = 4 pi – 8.

For Ch. 10, Lesson 2, Set III number 4 asks for rectangles with a ratio of 3/4. The key says there are 4 rectangles that have dimensions of 1.5×2. ABHG is correct, but the other three rectangles seem to be wrong. The key lists BDJI (which doesn’t even make a rectangle), CEKI (which is a 1.5×3 rectangle), and DFLJ (which is also a 1.5×3 rectangle). Can you confirm the correct rectangles are ABHG, CDJI, and EFLK? I know it seems obvious, but just want to make sure I’m not missing something here.

Dr. Callahan Wrote:

You are correct. This looks like a typo. The original solutions manual (titled “Enhanced Teacher’s Guide for Geometry – ISBN: 978-0716756071) had it correct. I have noticed a few places that the answers in the newer solutions manual have typos.

If you are looking for details on for a transcript for Jacobs Geometry Course, this description should do the trick.

Geometry is a branch of mathematics that deals with the understanding of the world around us by using measurement, properties, and relationships of points, lines, angles, surfaces, and solids. This course covers Euclidean geometry – which is a mathematical system where we assume a small set of truths (axioms) and from them, we deduce through logic, many other propositions (theorems). This course emphasizes the concept of proofs, but in a reachable way that helps the student learn both the logic and the geometrical mathematics. Students who complete Geometry should take Algebra II with Trig (aka precalculus) next. Concepts from this course show up on the ACT and the SAT.

Topics Covered in this Course:

Deductive Reasoning

Lines and Angles

Congruence

Inequalities

Parallel Lines

Quadrilaterals

Transformations

Area

Similarity

The Right Triangle

Circles

Regular Polygons and the Circle

Geometric Solids

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