**Question from Anya**

**Answer by Dr.Callahan**

Course: Geometry

Chapter/Lesson/Problem11 test7b

Issue: I’m supposed to find Angle APM. To find the angle, I used tan APM=20/70, which gives 15.9 degrees. The solutions manual used sin APM=20/70, which gives 16.6 degrees. Sine is opposite/hypotenuse. However, it seems to me that the given measurements of the problem are opposite side (20) to the adjacent side (70). Which is correct? Thank you!

Yes, you are correct. That should be tangent as you stated.

tan(APM) = 20/70

**Question from Joy:**

We are in Geometry 3 rd edition. Chapter 14 lesson 2 number 22-23. Page 582.

How do you get 108?

The answer in key says 3 x 180/5? Why? I think I missed something important yet simple. I was thinking divide 360/5. What an I doing wrong? Thanks!

**Answer from Dr. Callahan:**

I have to admit – I could not find this in the book. I think it SHOULD be there – but could not find it.

The answer is the a triagle has interior angles that add up to 180 (we know that – right)

So each time we add a side (triangle to square) we add 180.

See here https://www.mathsisfun.com/geometry/interior-angles-polygons.html

So in #22, he is saying we have 180 3 times (triangle plus 2 sides adding 2 more 180s) as the total angles and then dived by the number of sides to get 108.

Again – I do not see this in the book.

Hope this helps

dwc

For Chap 13, Lesson 6, #32, the basis for the answers is the figure for #6. If we look carefully at the grid, applying the Pythagorean Theorem gives XY^2 = 2^2 + 2^2 = 8, so XY = sqrt8 = 2sqrt2. YZ^2 = 1^2 + 1^2 = 2, so YZ =sqrt2. Therefore XY = 2YZ.

Harold Jacobs

—

—

The 3rd edition of the Harold Jacobs Geometry textbook has gone through three different printings with 3 different covers and ISBNs. If you are picking a text and looking at used options, it can be confusing. So let me try to help.

First, all 3 versions are basically the same – as long as they say 3rd edition. They look like the photos below.

The original published by Freeman – ISBN: 978-0-7167-4361-3 and the corresponding Teachers Guide which contains the solutions to the problems. This book had a separate Test Bank for tests.

The second printing published by My Father’s World – ISBN: 978-1-61999-109-5 and the corresponding Teachers Guide which contained the tests and the Answer Key.

The third printing published by Master Books – ISBN: 9787-1-68344-020-8. This is the latest and if you are buying new, this is what you are getting. The tests are in the Teacher’s Guide and the answers are in the Solutions Manual. You will need all 3 books for the course.

All 3 of the printings will work with the AskDrCallahan videos. The various printings have minor changes in page numbers, drawings, and some problems have changed – but the basic content remains the same. But, just to be more confusing, the videos come in 3 different packages. All are the same content but they might look different. All require the student to have one of the 3 textbooks, the tests, and a set of solutions.

**1 – The original DVDs published by us (AskDrCallahan)** -ISBN:978-0-615-27810-0

**2 – The latest version of the DVDs was published by Master Books** – UPC: 713438-110236-8

**3 – The online version**, offered by us only, have the same content and bypass the need for DVDs and a DVD player. They are the same content as on the DVD. The online videos come in two options.

- Monthly option – Pay for the course monthly and cancel anytime by logging into your AskDrCallahan account (or email us to cancel). This option is perfect if you think you will need just a few months.
- Lifetime access – If you need a full year, or have siblings who might use the course later, then this is your option. One price one time.

Chap 8 review

#32

We aren’t sure how the answer would be 24mm.

This is not explained well in the textbook.

First – the translation is the movement of the bat from position B to position C (see chap 8, Lesson 2) A translation is two rotations around a parallel line – or in other words, we moved it over from one place to another.

So he is asking, how far did it move. Or, what is the length of the black line moving from B to C.

Since we can measure the bat to be about 42 mm (with a ruler), the length of the black line is about 24 mm using the same ruler.

**Question from Courtney**

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.

Look for the following material or heading in the contents.

- Reasoning and Proof

· Proofs

· Deductive reasoning

· Direct and indirect proofs - Lines

· Parallel and Perpendicular Lines

· Angles - Triangles

· Congruent

· Isosceles

· Equilateral

· ASA and SAS - Quadrilaterals

· Parallelograms

· Rectangles

· Squares

· Trapezoids - Area

· Squares

· Rectangles

· Triangles - 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.

The book has a problem

(x-3)(x^2 – 7x – 2)

which results in an answer of

x^3 – 10x^2 – 2x +19x + 6

The solution is incorrect in the new solutions manual ( the one with a bee on the cover)

However, it is correct in the old solutions manual -the one with a chess set on the cover.

**Geometry Designed for Understanding**

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.

Geometry Teaching Videos: Approximately 4 hours of video instruction following the Jacobs 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!

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.

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.

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.

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

: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.

- Can I use the second edition textbook in this course?
- Should I take algebra II before geometry?
- Does it contain proofs? (Euclidean)
- How do I get support?

**Geometry Designed for Understanding**

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.

Geometry Teaching Videos: Approximately 4 hours of video instruction following the Jacobs 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!

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.

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.

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

: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.

- Can I use the second edition textbook in this course?
- Should I take algebra II before geometry?
- Does it contain proofs? (Euclidean)
- How do I get support?