Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 3
Math
Unit 3
10th Grade
Lesson 3 of 18
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Lesson Notes
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Verify that dilations result in congruent angles and proportional line segments.
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
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Identify if the following statement is always, sometimes, or never true. Provide examples or criteria that support your reasoning.
“A dilation of an angle marked by two line segments will stretch or shrink the measure of the angle by the scale factor."
Describe whether each statement is true or false.
Below is rectangle $$A$$ that has been dilated by a scale factor of 1.5 to form rectangle $$B$$. Find the length of the diagonal in rectangle $$B$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Below is a figure, $$C$$, and its dilation, $$D$$, by a factor of $${\frac{4}{3}}$$.Â
Next
Divide a line segment into equal sections using 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
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.
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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.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.
Solve real-life problems with two different centers of dilation.
G.SRT.B.4G.SRT.B.5
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