Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 18
Math
Unit 3
10th Grade
Lesson 18 of 18
Jump To
Lesson Notes
There was an error generating your document. Please refresh the page and try again.
Generating your document. This may take a few seconds.
Are you sure you want to delete this note? This action cannot be undone.
Solve real-life problems with two different centers of dilation.
The core standards covered in this lesson
G.SRT.B.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.B.5 — Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
The foundational standards covered in this lesson
8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Eliot is playing football at night when two spotlights come on.
Part A: Draw a diagram to represent this situation. Be sure to label all quantities.
Part B: What is the total length of Eliot’s shadows. Explain your reasoning below.
Part C: Suppose Eliot walks in a straight line toward one of the floodlights. How does this movement change the total length of Eliot’s shadows?
Deducting Relationships: Floodlight Shadows from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Oct. 20, 2017, 10:16 a.m..
Topic A: Dilations off the Coordinate Plane
Describe properties of scale drawings.
Standards
G.SRT.A.2
Define and describe the characteristics of dilations. Dilate figures using constructions when the center of dilation is not on the figure.
G.CO.A.2G.SRT.A.2G.SRT.A.3
Verify that dilations result in congruent angles and proportional line segments.
Divide a line segment into equal sections using dilation.
G.CO.D.12G.SRT.A.1.AG.SRT.A.1.B
Dilate a figure from a point on the figure. Use the properties of dilations with respect to parallel lines to verify dilations and find the center of dilation.
G.CO.D.12G.SRT.A.1.AG.SRT.A.2
Prove that a line parallel to one side of a triangle divides the other two sides proportionally.
G.CO.C.10G.SRT.B.4G.SRT.B.5
Identify measurements in dilated figures with the center of dilation on the figure directly and algebraically.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Dilations on the Coordinate Plane
Dilate a figure on the coordinate plane when the center of dilation is the origin.
G.CO.A.2G.SRT.A.2
Dilate a figure when the center of dilation is not the origin. Determine center of dilation given the original and dilated figure.
Topic C: Defining Similarity
Define similarity transformation as the composition of basic rigid motions and dilations. Describe similarity transformation applied to an arbitrary figure.
G.SRT.A.2G.SRT.B.5
Prove that all circles are similar.
G.C.A.1
Prove angle-angle criterion for two triangles to be similar.
G.SRT.A.3
Use angle-angle criterion to prove two triangles to be similar.
Develop the side splitter theorem and side-angle-side similarity criteria, and use these in the solution of problems.
G.SRT.B.5
Topic D: Similarity Applications
Develop the angle bisector theorem based on facts about similarity and congruence, and use this in the solution of problems.
Use the side-side-side criteria for similarity and other similarity and congruence theorems in the solution of problems.
Solve for measurements involving right triangles using scale factors and ratios.
G.SRT.B.4G.SRT.B.5
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
We've got you covered with rigorous, relevant, and adaptable math lesson plans for free