HIGH SCHOOL
- ACT Tutoring
- SAT Tutoring
- PSAT Tutoring
- ASPIRE Tutoring
- SHSAT Tutoring
- STAAR Tutoring
GRADUATE SCHOOL
- MCAT Tutoring
- GRE Tutoring
- LSAT Tutoring
- GMAT Tutoring
- AIMS Tutoring
- HSPT Tutoring
- ISAT Tutoring
- SSAT Tutoring
Search 50+ Tests
Loading Page
math tutoring
- Elementary Math
- Pre-Calculus
- Trigonometry
science tutoring
Foreign languages.
- Mandarin Chinese
elementary tutoring
- Computer Science
Search 350+ Subjects
- Video Overview
- Tutor Selection Process
- Online Tutoring
- Mobile Tutoring
- Instant Tutoring
- How We Operate
- Our Guarantee
- Impact of Tutoring
- Reviews & Testimonials
- Media Coverage
- About Varsity Tutors
Common Core: High School - Geometry : Similarity, Right Triangles, & Trigonometry
Study concepts, example questions & explanations for common core: high school - geometry, all common core: high school - geometry resources, example questions, example question #1 : dilations given center and scale factor: ccss.math.content.hsg srt.a.1.
If the red figure is an object and the blue figure is an object after dilation, what is the scale factor?
The best way to solve for the scale factor is to find the same vertex from each object, and divide their components.
Let's divide the x-coordinates together.
Since we are going from the smaller object to the larger object, we know that our scale factor is going to be greater than one.
So our final answer is going to be.
Example Question #2 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Example Question #3 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Example Question #4 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Example Question #5 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
If the blue figure is an object and the red is an object after dilation, what is the scale factor?
Since we are going from the larger object to the smaller object, we know that our scale factor is going to be less than one.
Example Question #1 : Similarity, Right Triangles, & Trigonometry
Example Question #7 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Example Question #8 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Example Question #9 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Example Question #10 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1
Report an issue with this question
If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.
DMCA Complaint
If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.
Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.
Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.
Please follow these steps to file a notice:
You must include the following:
A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.
Send your complaint to our designated agent at:
Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105
Or fill out the form below:
Contact Information
Complaint details.
- About the Standards
- Voices of Support
- The Standards
- Introduction
- How to read the grade level standards
- Standards for Mathematical Practice
Kindergarten
- Counting & Cardinality
- Operations & Algebraic Thinking
- Number & Operations in Base Ten
- Measurement & Data
- Number & Operations—Fractions¹
- Number & Operations in Base Ten¹
- Number & Operations—Fractions
- Ratios & Proportional Relationships
- The Number System
- Expressions & Equations
- Statistics & Probability
High School: Number & Quantity
- The Real Number System
- Quantities*
- The Complex Number System
- Vector & Matrix Quantities
High School: Algebra
- Seeing Structure in Expressions
- Arithmetic with Polynomials & Rational Expressions
- Creating Equations*
- Reasoning with Equations & Inequalities
High School: Functions
- Interpreting Functions
- Building Functions
- Linear, Quadratic, & Exponential Models*
- Trigonometric Functions
High School: Modeling
High school: geometry.
- Similarity, Right Triangles, & Trigonometry
- Expressing Geometric Properties with Equations
- Geometric Measurement & Dimension
- Modeling with Geometry
High School: Statistics & Probability
- Interpreting Categorical & Quantitative Data
- Making Inferences & Justifying Conclusions
- Conditional Probability & the Rules of Probability
- Using Probability to Make Decisions
Note on courses & transitions
- Courses & Transitions
Mathematics Glossary
Mathematics » high school: geometry » similarity, right triangles, & trigonometry, standards in this domain:, understand similarity in terms of similarity transformations.
- A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
- G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity
- G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
- G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles
- G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
- G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
Apply trigonometry to general triangles
- G-SRT.9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
- G-SRT.10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
- G-SRT.11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
- Get Involved
- ©2012 Common Core State Standards Initiative
- Terms of Use
- Public License
Calcworkshop
Similar Right Triangles Fully Explained w/ 9 Examples!
// Last Updated: January 21, 2020 - Watch Video //
In today’s geometry lesson, you’re going to learn all about similar right triangles.
Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)
More specifically, you’re going to see how to use the geometric mean to create proportions, which in turn help us solve for missing side lengths.
Let’s get started!
How are right triangles and the geometric mean related?
The two legs meet at a 90° angle, and the hypotenuse is the side opposite the right angle and is the longest side.
Right Triangle Diagram
The geometric mean of two positive numbers a and b is:
Geometric Mean of Two Numbers
And the geometric mean helps us find the altitude of a right triangle! In fact, the geometric mean, or mean proportionals, appears in two critical theorems on right triangles.
Geometric Mean Theorems
In a right triangle, if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, then the length of the altitude is the geometric mean of the lengths of the two segments.
Altitude Rule
Additionally, the length of each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg, as ck-12 accurately states.
But what do these theorems really mean?
They help us to create proportions for finding missing side lengths!
Let’s look at an example!
How To Solve Similar Right Triangles
In the figure below, we are being asked to find the altitude, using the geometric mean and the given lengths of two segments:
Using Similar Right Triangles
In the video below, you’ll learn how to deal with harder problems, including how to solve for the three different types of problems:
- Missing Altitude
- Missing Leg
- Missing Segment of a Leg
Video – Lesson & Examples
- Introduction
- 00:00:29 – 2 Important Theorems
- Exclusive Content for Member’s Only
- 00:13:21 – What is the length of the altitude drawn to the hypotenuse? (Examples #1-6)
- 00:25:47 – The altitude to hypotenuse is drawn in a right triangle, find the missing length (Examples #7-9)
- Practice Problems with Step-by-Step Solutions
- Chapter Tests with Video Solutions
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Get My Subscription Now
Still wondering if CalcWorkshop is right for you? Take a Tour and find out how a membership can take the struggle out of learning math.
Common Core Geometry Math (Worksheets, Homework, Lesson Plans)
Related Topics: Common Core Math Resources, Lesson Plans & Worksheets for all grades Common Core Math Video Lessons, Math Worksheets and Games for Geometry Common Core Math Video Lessons, Math Worksheets and Games for all grades
Looking for video lessons that will help you in your Common Core Geometry math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Geometry students?
The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Geometry Worksheets.
These Lesson Plans and Worksheets are divided into five modules.
Geometry Homework, Lesson Plans and Worksheets
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
Common Core Geometry - Unit #8 Right Triangle Trigonometry
Description
This 6-lesson unit contains lessons that develop and apply right triangle trigonometry. Initial lessons emphasize the connection of trigonometry to similar right triangles. Trigonometric ratios are used in later lessons to find missing sides and missing angles in right triangles. Two lessons on applying trigonometric ratios are included.
To access the lesson videos on YouTube, use your smartphone or tablet to scan the QR code at the top of each lesson.
Questions & Answers
Emathinstruction.
- We're hiring
- Help & FAQ
- Privacy policy
- Student privacy
- Terms of service
- Tell us what you think
Geometry: Common Core (15th Edition)
By charles, randall i., chapter 7 - similarity - 7-3 providing triangles similar - practice and problem-solving exercises - page 455: 11, work step by step, update this answer.
You can help us out by revising, improving and updating this answer.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
VIDEO
COMMENTS
In this lesson we first see why two right triangles that have an acute angle in common must be similar. We then notice that the ratios of relatively position...
Find step-by-step solutions and answers to Geometry Common Core - 9780133185829, as well as thousands of textbooks so you can move forward with confidence. ... Right Triangles and Trigonometry. Section 8-1: The Pythagorean Theorem and Its Converse. ... Perimeters and Areas of Similar Figures. Page 642: Mid Chapter Quiz. Section 10-5 ...
Unit 8 - Right Triangle Trigonometry. Lesson 1. Similar Right Triangles. LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. Lesson 2.
Geometry: Common Core (15th Edition) answers to Chapter 7 - Similarity - 7-4 Similarity in Right Triangles - Practice and Problem-Solving Exercises - Page 465 20 including work step by step written by community members like you. Textbook Authors: Charles, Randall I., ISBN-10: 0133281159, ISBN-13: 978--13328-115-6, Publisher: Prentice Hall
in similar right triangles • Use the side splitter and triangle-angle-bisector theorem • Use the Pythagorean theorem and its converse Standards Solution Common Core Geometry Lessons: • Applications of the Pythagorean Theorem and Foundational Trigonometry • Dilations to Discover properties of Similar Triangles • Discovering More
Exercise 14. Exercise 15. Exercise 16. Exercise 17. Exercise 18. Exercise 19. Exercise 20. Exercise 21. Find step-by-step solutions and answers to Geometry, Common Core Edition - 9780547647098, as well as thousands of textbooks so you can move forward with confidence.
Free practice questions for Common Core: High School - Geometry - Similarity, Right Triangles, & Trigonometry. Includes full solutions and score reporting. ... Common Core: High School - Geometry Help » Similarity, Right Triangles, & Trigonometry Example Question #1 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1.
G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (1) In G.CO.A.2 we discussed isometric transformations and non-isometric transformations and there we introduced dilation. This week is about really about exploring the dilation transformation -- its properties, graphing ...
Find step-by-step solutions and answers to Big Ideas Math Geometry: A Common Core Curriculum - 9781608408399, as well as thousands of textbooks so you can move forward with confidence. ... Right Triangles and Trigonometry. Section 9.1: The Pythagorean Theom . Section 9.2: Special Right Triangles. Section 9.3: Similar Right Triangles. Page 486 ...
Define trigonometric ratios and solve problems involving right triangles. G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
Similar Right Triangles. Fully Explained w/ 9 Examples! In today's geometry lesson, you're going to learn all about similar right triangles. More specifically, you're going to see how to use the geometric mean to create proportions, which in turn help us solve for missing side lengths. Let's get started!
Now you are ready to create your Geometry Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This Geometry Worksheet will produce eight problems for working with similar right triangles. You may select the types of side lengths used in each problem.
Math; Algebra; Algebra questions and answers; Trece RIGHT TRIANGLES AND SIMILARITY COMMON CORE GEOMETRY HOMEWORK MEASUREMENT AND CONSTRUCTION 1. Given right triangle ABC below with right angle C, construct the altitude CD to hypotenuse AB.Leave all construction marks. If you can't recall how to do this construction, see Unit #4.Lesson #3.
Find step-by-step solutions and answers to Geometry (Common Core) - 9780547647142, as well as thousands of textbooks so you can move forward with confidence. ... Prove Triangles Similar by SSS and SAS. Section 6.6: Perform Similarity Transformations. Page 412: ... Use Similar Right Triangles. Section 7.4: Special Right Triangles. Page 459 ...
In this lesson we explore and justify why the altitude drawn from the right angle of a right triangle to its hypotenuse created two additional similar right ...
Geometry: Common Core (15th Edition) answers to Chapter 7 - Similarity - 7-4 Similarity in Right Triangles - Practice and Problem-Solving Exercises - Page 465 9 including work step by step written by community members like you. Textbook Authors: Charles, Randall I., ISBN-10: 0133281159, ISBN-13: 978--13328-115-6, Publisher: Prentice Hall
Lesson 1: Construct an Equilateral Triangle ( Video Lesson) Lesson 2: Construct an Equilateral Triangle ( Video Lesson) Lesson 3: Copy and Bisect an Angle ( Video Lesson) Lesson 4: Construct a Perpendicular Bisector ( Video Lesson) Lesson 5: Points of Concurrencies ( Video Lesson) Unknown Angles. Topic B Overview.
Geometry: Common Core (15th Edition) answers to Chapter 7 - Similarity - 7-3 Providing Triangles Similar - Practice and Problem-Solving Exercises - Page 456 15 including work step by step written by community members like you. Textbook Authors: Charles, Randall I., ISBN-10: 0133281159, ISBN-13: 978--13328-115-6, Publisher: Prentice Hall
Be the first to ask eMATHinstruction a question about this product. This 6-lesson unit contains lessons that develop and apply right triangle trigonometry. Initial lessons emphasize the connection of trigonometry to similar right triangles. Trigonometric ratios are used in later lessons to find missing sides and missing angles in right triangles.
Find step-by-step solutions and answers to Geometry - 9780547315171, as well as thousands of textbooks so you can move forward with confidence. ... Use Proportions to Solve Geometry Problems. Section 6.3: Use Similar Polygons. Page 380: Mixed Review of Problem Solving. ... Use Similar Right Triangles. Section 7.4: Special Right Triangles. Page ...
Du SIMILAR RIGHT TRIANGLES COMMON CORE GEOMETRY HOMEWORK PROBLEM SOLVING 1. In the following diagram. AKFG is im ALMN. Find the following is Expo a decimals to the mere hundredth Show with that leads to your answer IN EN (b) MNM o 13 5 12 AN 1 L 2 bis known that ARST-AXTI RS = 18.
Geometry: Common Core (15th Edition) answers to Chapter 7 - Similarity - 7-3 Providing Triangles Similar - Practice and Problem-Solving Exercises - Page 455 11 including work step by step written by community members like you. Textbook Authors: Charles, Randall I., ISBN-10: 0133281159, ISBN-13: 978--13328-115-6, Publisher: Prentice Hall
Find step-by-step solutions and answers to Core Connections Geometry - 9781603281089, as well as thousands of textbooks so you can move forward with confidence. ... Constant Ratios in Right Triangles. Section 4.1.2: Connecting Slope Ratios to Specific Angles. Section 4.1.3: ... Area Ratios of Similar Figures. Section 8.2.2: Ratios of Similarity ...