Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 17
Math
Unit 3
10th Grade
Lesson 17 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 for measurements involving right triangles using scale factors and ratios.
The core standards covered in this lesson
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
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
What do you notice?
What is the height of the tree?
Geometry > Module 2 > Topic C > Lesson 16 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Draw a diagram that represents the following information.
Given the following information: $${\overline{AB} \parallel \overline{DE}}$$
$${A,D,C}$$ are collinear $${B,E,C}$$ are collinear $${DE=12m}$$ $${EC=8m}$$ $${AB=18m}$$ $${CB=12m}$$
Identify three ratios between side lengths that are proportional.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Dennis needs to fix a leaky roof on his house but does not own a ladder. He thinks that a 25 ft. ladder will be long enough to reach the roof, but he needs to be sure before he spends the money to buy one. He chooses a point $$P$$ on the ground where he can visually align the roof of his car with the edge of the house roof. Help Dennis determine if a 25 ft. ladder will be long enough for him to safely reach his roof.
en
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Solve real-life problems with two different centers of dilation.
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.
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