transformations and their link to congruency and...

Transformations and Their Link to Congruency and Similarity

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Teacher Lesson Plan Lesson: Day 2 – Supplement Lesson Transformations and Their Link to Congruency and Similarity CC Standards 8.G.1 Verify experimentally the properties of rotations, reflections, and translations: 8.G.1.a Lines are taken to lines, and line segments to line segments of the same length. 8.G.1.b Angles are taken to angles of the same measure. 8.G.1.c Parallel lines are taken to parallel lines. 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.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.

Calculator - No Objective TSW… learn about the properties of congruent and similar figures and how they are linked to transformations. Mathematical Practices #1 Make sense of problems and persevere in solving them. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning Teacher Input Bellwork: Review bellwork. Homework: Review important problems assigned the previous night. Introduction: Introduce as directed in the PowerPoint. See real-world connection to congruent and similar. Lesson: Teach as directed in the PowerPoint. Be sure to look at the notes on each slide for additional

instruction and answers. Practice Classwork Pages 2-5 Homework Pages 6-7 Closure Teacher selected.

http://www.corestandards.org/Math/Content/8/G/A/1/

http://www.corestandards.org/Math/Content/8/G/A/1/a/

http://www.corestandards.org/Math/Content/8/G/A/1/b/

http://www.corestandards.org/Math/Content/8/G/A/1/c/

http://www.corestandards.org/Math/Content/8/G/A/2/


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Classwork Name_______________________________________ Date_________________ Period_______

1) Fill in the blank with the word similar or congruent. ____________ figures have the same shape and are the same size. ____________ figures have the same shape but are different sizes. 2) Name the three types of transformations that are congruency transformations?

3) Which transformation is a similarity transformation? 4) Answer the following questions regarding the congruent figures below.

Which angle is congruent to C? _____ Which side is congruent to CA? _____ Which angle is congruent to A? _____ Which side is congruent to AB? _____ Which angle is congruent to B? _____ Which side is congruent to BC? _____ 5) Eight triangles are shown on the coordinate plane.

Part A Which of these triangles could be the image of ∆ABC after a sequence of translations, reflections, and/or rotations? Circle ALL that apply.

∆R ∆T ∆U ∆V ∆S ∆P ∆Q Part B Which triangle could represent a dilation of ∆ABC? after a translation has occurred? ∆_______


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6) Are these two triangles congruent, similar, or neither? Explain your reasoning. _____________ Explain: ____________________________________________ ____________________________________________ ____________________________________________ ____________________________________________ 7) Are these two triangles congruent, similar, or neither? Explain your reasoning. _____________ Explain: ____________________________________________ ____________________________________________ ____________________________________________ ____________________________________________ 8) Are these two triangles congruent, similar, or neither? Explain your reasoning. _____________ Explain: ____________________________________________ ____________________________________________ ____________________________________________ ____________________________________________


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9) Name the type of transformation performed as a translation, reflection, rotation, or dilation. ______________ ______________ ______________

______________ ______________ ______________ 10) The pre-image was rotated to form the image as seen on the figures below. What is the degree of rotation going clockwise? How about counter-clockwise? Clockwise _______̊ Clockwise _______̊ Counter-clockwise _______̊ Counter-clockwise _______̊


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11) Below are two reflections. Indicate if the reflection was performed over the x-axis or the y-axis. ______________ ______________ In the figures above, how can you tell which is the pre-image (original) and which is the image (new)? ____________________________________________ ____________________________________________ ____________________________________________ ____________________________________________ 12) Was the dilation performed on ∆ABC an enlargement or reduction?


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Homework Name_______________________________________ Date_________________ Period_______

11) Name each transformation. Then circle the correct answer stating whether the resulting image is congruent or similar to the original.

______________ ______________ ______________ ______________ Congruent or Similar Congruent or Similar Congruent or Similar Congruent or Similar

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12. Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement.

13. Is this reflection from figure A to figure B across the x-axis or y-axis?

14. Name the degree of rotation as 90°, 180°, 270°, or 360°.

Clockwise from figure A to figure Z. _____°

Counter-Clockwise from figure A to figure Z. _____°

Counter-clockwise from figure Z to figure B. _____°

Clockwise from figure Z to figure B. _____°

Clockwise from figure B back around to figure B again. _____°


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Answer Keys


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Classwork Name___________ Answer Key___________________ Date_________________ Period_______

1) Fill in the blank with the word similar or congruent. ___Congruent_______ figures have the same shape and are the same size. ___Similar_______ figures have the same shape but are different sizes. 2) Name the three types of transformations that are congruency transformations? translations, reflections, and rotations

3) Which transformation is a similarity transformation? dilations 4) Answer the following questions regarding the congruent figures below.

Which angle is congruent to C? ∠H Which side is congruent to CA? 𝑯𝑰̅̅ ̅̅ Which angle is congruent to A? ∠ I Which side is congruent to AB? 𝑰�̅� Which angle is congruent to B? ∠J Which side is congruent to BC? 𝑱𝑯̅̅̅̅ 5) Eight triangles are shown on the coordinate plane.

Part A Which of these triangles could be the image of ∆ABC after a sequence of translations, reflections, and/or rotations? Circle ALL that apply.

∆R ∆T ∆U ∆V ∆S ∆P ∆Q Part B Which triangle could represent a dilation of ∆ABC? after a translation has occurred? ∆__V__


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6) Are these two triangles congruent, similar, or neither? Explain your reasoning. Similar. Similar figures are the same shape but are different sizes. In similar figures the angles will match up to the angles, however the sides will NOT match up to the sides. On these two figures, the arcs indicate that the angles are the same measurement. The side lengths are shown to be different. 7) Are these two triangles congruent, similar, or neither? Explain your reasoning. Congruent. Congruent figures are the same shape and the same size. Angles match up to angles and sides match up to sides. These two triangles meet that criteria. 8) Are these two triangles congruent, similar, or neither? Explain your reasoning. Neither. The may appear similar, but they are not. The angle measurements do not match up.


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9) Name the type of transformation performed as a translation, reflection, rotation, or dilation. translation dilation reflection reflection rotation translation 10) The pre-image was rotated to form the image as seen on the figures below. What is the degree of rotation going clockwise? How about counter-clockwise? Clockwise ___180____̊ Clockwise ___270____̊ Counter-clockwise ___180____̊ Counter-clockwise ___90____̊


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11) Below are two reflections. Indicate if the reflection was performed over the x-axis or the y-axis. x-axis y-axis In the figures above how can you tell which is the pre-image (original) and which is the image (new)? The image is labeled using prime notation symbols such as A’B’C’D’ 12) Was the dilation performed on ∆ABC an enlargement or reduction? enlargement


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Homework Name_________ Answer Key_______________________ Date_________________ Period_______

11) Name each transformation. Then circle the correct answer stating whether the resulting image is congruent or similar to the original.

rotation dilation translation reflection ______________ ______________ ______________ ______________ Congruent or Similar Congruent or Similar Congruent or Similar Congruent or Similar

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12. Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement.

reduction

13. Is this reflection from figure A to figure B across the x-axis or y-axis?

y-axis

14. Name the degree of rotation as 90°, 180°, 270°, or 360°.

Clockwise from figure A to figure Z. 90°

Counter-Clockwise from figure A to figure Z. 270°

Counter-clockwise from figure Z to figure B. 180°

Clockwise from figure Z to figure B. 180°

Clockwise from figure B back around to figure B again. 360°

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