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Unit 7 – Dilations and Similarity

LESSON/HOMEWORK

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

Dilations in the Coordinate Plane

Dilations and Angles

Similarity Criteria

Reasoning with Similarity

More Similarity Reasoning

The Side Splitter Theorem

Partitioning a Line Segment

The Medians of a Triangle

Right Triangles and Similarity

Proving the Pythagorean Theorem (no hmwk)

Unit Review

Unit 7 Review – Dilations and Similarity

UNIT REVIEW

EDITABLE REVIEW

Unit 7 Assessment Form A

EDITABLE ASSESSMENT

Unit 7 Assessment Form B

Unit 7 Assessment Form C

Unit 7 Assessment Form D

Unit 7 Exit Tickets

Unit 7 Mid-Unit Quiz (Through Lesson #5) – Form A

Unit 7 Mid-Unit Quiz (Through Lesson #5) – Form B

Unit 7 Mid-Unit Quiz (Through Lesson #5) – Form C

Unit 7 Mid-Unit Quiz (Through Lesson #5) – Form D

U07.AO.01 – Further Practice with Similarity

EDITABLE RESOURCE

U07.AO.02 – Lesson 10.5.The Centroid of a Triangle (Activity)

U07.AO.03 – Practice – Right Triangles and Similarity

U07.AO.04 – Similarity Transformations Practice

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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 #2 : Similarity, Right Triangles, & Trigonometry

Example Question #3 : 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 #5 : Similarity, Right Triangles, & Trigonometry

Example Question #4 : Dilations Given Center And Scale Factor: Ccss.Math.Content.Hsg Srt.A.1

Example Question #9 : Similarity, Right Triangles, & Trigonometry

Example Question #10 : Similarity, Right Triangles, & Trigonometry

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Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.   Again paralleling the same process we did with congruence, first we define the motion in the plane, the dilation (G.SRT.A.1), then we look at what it means to be similar (G.SRT.A.2) and then finally we will determine the similarity criteria. This objective only mentions the AA criteria but I feel that we should look at SAS and SSS proportionality criteria as well.             SKILLS The student will be able to prove two triangles to be similar using the minimum requirements of AA, SAS and SSS.   The student will be able to use the properties of similarity transformations to establish the AA, SAS and SSS criterion for two triangles to be similar.   THE BIG IDEA Other than congruence... there is no bigger idea than similarity. Ratios in diagrams constantly show up and at the heart of those most often is the hidden similarity relationship. Similarity shows up in all areas from this point forward - partitioning a segment, angle values in a circle, parallel lines, mid-segments, etc... the list just keep going on and on. Recognizing and using the concepts of similarity is essential for success in geometry. TRAPS & PITFALLS When we did proof of congruence we looked for 'hidden' items in the diagram that weren't specifically mentioned in the given such as vertical angles, a common side, angles formed by parallel lines, etc... These same items help us succeed in proof of similarity. The one that is most 'hidden' to the student eye is the common angle. A very common setup for similar triangles is to have an overlapping angle. So in the diagram below ∠A is common in both triangles - this is often missed by students. PAST CONNECTIONS In G.CO.A.8 we looked at the criteria for triangle congruence, and now we are doing the same thing but with establishing similarity between figures. Much of the same logic and work takes place for both of these processes. FUTURE CONNECTIONS As mentioned in the big idea, establishing figures to be similar is a very common theme throughout the rest of the year. Similarity of triangles shows up very very often because the only required knowledge is two corresponding congruent angles, and this happens in many different cases, it happens almost automatically anytime parallel lines are present in the diagram. MY REFLECTIONS (over line l ) Nothing really hidden in this objective, we have been teaching similar proof and specifically AA from the beginning of time. I found the students to picked it up quickly because how 'similar' it is to what we did with congruence. Most proofs of this type are AA and not SAS or SSS even through they are viable ways to also establish similarity. I think they are not used as much because to get the information into the diagram it is difficult, it would probably require giving lengths and I can't recollect ever seeing that. Usually the given expressly gives that the ratios exist which takes any adventure out of it. 334 IMAGES SOLVED: Name: Date: More SiMILARITY REASONING COMMON CORE GEOMETRY Solved Date: TRIANGLE CONGRUENCE THEOREMS COMMON CORE G Co C 9 Worksheet 1 Geometry Common Core Answers Using Similar Triangles (examples, solutions, videos, lessons Solved SIMILARITY COMMON CORE GEOMETRY HOMEWORK PROBLEM Du SIMILAR RIGHT TRIANGLES COMMON CORE GEOMETRY VIDEO Geometry Common Core Objective Overview G-SRT.C.8 Similarity Similarity Prac.set 1.3 part 2. Geometry 10 class All of iGCSE Similarity In Just 40 Minutes! Common Core Geometry.Unit #6.Lesson #2.Properties of Parallelograms Common Core Geometry.Unit #9.Lesson #4.Intersecting Chords COMMENTS Unit 7 - Dilations and Similarity - eMATHinstruction Common Core Geometry; Common Core Algebra II; ... LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. ... More Similarity Reasoning. LESSON/HOMEWORK. Geometry Common Core Edition - 1st Edition - Solutions and ... Our resource for Geometry Common Core Edition includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers to ... Geometry Common Core - 1st Edition - Solutions and Answers ... Now, with expert-verified solutions from Geometry Common Core 1st Edition, you’ll learn how to solve your toughest homework problems. Our resource for Geometry Common Core includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. Ccgeo.unit 7.lesson 7.more Similarity Reasoning key Name: _____ Date: _____ MORE SIMILARITY REASONING COMMON CORE GEOMETRY Reasoning with similar triangles can be challenging for students, especially because it is not always obvious when two triangles have the same shape, but not the same size. In today's lesson, we will need a bit of reasoning that you've seen before, but perhaps didn't ... Common Core: High School - Geometry : Similarity, Right ... Free practice questions for Common Core: High School - Geometry - Similarity, Right Triangles, & Trigonometry. Includes full solutions and score reporting. High School Geometry Common Core G.SRT.A.3 - Similarity ... (1) The student will be able to prove two triangles to be similar using the minimum requirements of AA, SAS and SSS. (2) The student will be able to use the properties of similarity transformations to establish the AA, SAS and SSS criterion for two triangles to be similar. assignment essay homework phd report resume review speech thesis