Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 9
Math
Unit 3
10th Grade
Lesson 9 of 18
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Dilate a figure when the center of dilation is not the origin. Determine center of dilation given the original and dilated figure.
The core standards covered in this lesson
G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.SRT.A.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.
The foundational standards covered in this lesson
8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Shown is the rectangle $${{ABCD}}$$ and the dilation of rectangle $${{ABCD}}$$ about point $$F$$ by a scale factor of $$3$$.
What is the relationship between the distance between $$FA$$ and $$FA'$$?
Dilate the figure below by a scale factor of $$2$$ about point $$A$$.
Given the figure and its dilation, determine the center of dilation.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
With a dilation of $${\frac{1}{2}}$$Â and a center of dilation at $${P(1,2)}$$, which of the following is true about the dilation of line segment $${\overline{AB}}$$Â with $${A(5,6)}$$Â and $${B(7,8)}$$?Â
a.   The rule to apply to the coordinate points will be $$(x,y)\rightarrow\left ( {\frac{1}{2}}x,{\frac{1}{2}}y \right )$$.
Â
b.   $${\overline{AB}}\parallel\overline{{A'}{B'}}$$
c.   Points $${A'}$$ and $${B'}$$ lie on the same ray as $$A$$ and $$B$$.Â
d.   To find point $${A'}$$, divide the distance between $$P$$ and $$A$$ in half.Â
e.   Point $${B'}$$ will be $${(3,5)}$$.
Lesson 8
Lesson 10
Topic A: Dilations off the Coordinate Plane
Describe properties of scale drawings.
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.Â
G.CO.A.2 G.SRT.A.2 G.SRT.A.3
Verify that dilations result in congruent angles and proportional line segments.
Divide a line segment into equal sections using dilation.Â
G.CO.D.12 G.SRT.A.1.A G.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.12 G.SRT.A.1.A G.SRT.A.2
Prove that a line parallel to one side of a triangle divides the other two sides proportionally.
G.CO.C.10 G.SRT.B.4 G.SRT.B.5
Identify measurements in dilated figures with the center of dilation on the figure directly and algebraically.
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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.2 G.SRT.A.2
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.2 G.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.
Solve real-life problems with two different centers of dilation.
G.SRT.B.4 G.SRT.B.5
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