Curriculum / Math / 10th Grade / Unit 3: Dilations and Similarity / Lesson 1
Math
Unit 3
10th Grade
Lesson 1 of 18
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Describe properties of scale drawings.
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
7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
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
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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
Below is an image of a bicycle.
Which of the images below appears to be scaled proportionally to the bicycle shown above and why?
The two triangles below are scaled figures of one another. Describe how you know this to be true.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The figures above are scaled well. Which of the following statements must be true? Select all that apply.
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.
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Define and describe the characteristics of dilations. Dilate figures using constructions when the center of dilation is not on the figure.
Topic A: Dilations off the Coordinate Plane
Standards
G.SRT.A.2
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.
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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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