Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 7
Math
Unit 3
10th Grade
Lesson 7 of 18
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Identify measurements in dilated figures with the center of dilation on the figure directly and algebraically.
The core standards covered in this lesson
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.1 — Verify experimentally the properties of rotations, reflections, and translations:
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson has only one anchor problem to allow for practice from previous lessons before moving on to the next topic of the unit.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Triangle $${ABC}$$ is dilated from point $$A$$ by a scale factor of $${2.5}$$. Below are some measurements:
$$m∠{ABC}=35^{\circ}$$ $$AB=4$$ $$AC=6$$
What is the length of $${\overline{BB'}}$$? If $${BC=x+2}$$, write an expression that describes the length of $${\overline{B'C'}}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Identify the strategy that the student below used to find the measure of $${BA}$$. Then, describe a different method for finding this value, describing how you know that the two triangles are dilations of one another.
Decimal Misconceptions? Meet similar triangles. by Michael Pershan is made available on Math Mistakes under the CC BY 3.0 license. © 2017 Math Mistakes, all rights reserved. Accessed Oct. 19, 2017, 2:01 p.m..
Lesson 6
Lesson 8
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
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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
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.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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