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9-12 Integrated Math 2 Unit 2 Lesson 7

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Unit 2, Lesson 7

Reasoning about Similarity with Transformations

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Integrated Math 2

Practice

Problem 1

Sketch a figure that is similar to this figure. Label side and angle measures.

<p><strong>Rhombus. Side lengths 12. Moving clockwise from top left corner, angle measures as follows: 30 degrees, 150 degrees, 30 degrees, 150 degrees.</strong></p>

Problem 2

Write 2 different sequences of transformations that would show that triangles and are similar. The length of is 6 units.

<p>Triangle A B C and A D E. Point D is located on side A C and point E is to the right of side A C. Side A B is 8, B C is 4, A C is 6, A D is 3, A E is 4, and D E is 2.</p>

Problem 3

ForLesson 6: Connecting Similarity and Transformations

What is the definition of similarity?

Problem 4

Select all figures that are similar to Parallelogram .

<p>Quadrilateral. All sides are 5. Upper left and lower right angles are 50 degrees and upper right and lower left angles are 130 degrees.</p> — Parallelogram

<p>Quadrilateral. All sides are 5. Upper left and lower right angles are 50 degrees and upper right and lower left angles are 130 degrees.</p> — Figure

<p>Quadrilateral. All sides are 3, left and right side angles are both 50 degrees and upper and lower angles are both 130 degrees.</p> — Figure

<p>Quadrilateral. All sides are 5. Upper left and lower right angles are 45 degrees. Upper right and lower left angles are 135 degrees.</p> — Figure

<p>Quadrilateral. Left and right side sides are 5, top and bottom sides are 3. Upper left and lower right angles are 50 degrees and upper right and lower left angles are 130 degrees.</p> — Figure

<p>Quadrilateral. Bottom side is 10, left side is 5. Base angles are both 50 degrees, upper angles are both 130 degrees.</p> — Figure

Figure
Figure

Problem 5

ForLesson 6: Connecting Similarity and Transformations

Find a sequence of rigid transformations and dilations that takes square to square .

<p>Squares A B C D and E F G H. A B C D has A upper left, base B C and left side A B is 5. E F G H has G above E, rests on E and right lower side E F is 2.</p>

Translate by the directed line segment , which will take to a point . Then rotate with center by angle . Finally, dilate with center by a scale factor of .

Problem 6

ForLesson 5: Splitting Triangle Sides with Dilation (Part 1)

Triangle is formed by connecting the midpoints of the sides of triangle . What is the perimeter of triangle ?

<p>Triangles A B C and D E F. D is the midpoint of segment A B. E is the midpoint of segment B C. F is the midpoint of segment A C. Line D E has length 2, Line E F has length 3, Line D F has line 4.<br>
</p>

Problem 7

ForLesson 12: Proofs about Quadrilaterals

Select the quadrilateral for which the diagonal must be a line of symmetry.

parallelogram
square
trapezoid
isosceles trapezoid

Problem 8

ForLesson 10: One Hundred Eighty

Triangles and are each translations of triangle .

<p>Large triangle BFE has small triangle ADC at its midpoints.</p>

Explain why angle has the same measure as angle .

Figure

Figure

Figure

Translate by the directed line segment , which will take to a point . Then rotate with center by angle . Finally, dilate with center by a scale factor of .

Dilate, using center , by a scale factor of .

Dilate, using center , by a scale factor of .