TRANSFORMATIONAL GEOMETRY

 

 

GEOMETRY DOMAIN

Topic one TRANSFORMATIONAL GEOMETRY

Review the Kahn Academy Youtube Introduction to transformational geometry.

Note the four types of transformations and describe each.

REFLECTIONS OR FLIP

TRANSLATIONS OR SLIDE

ROTATIONS OR TURN

DILATIONS OR ENLARGEMENT/REDUCTIONS

 

COORDINATE PLANE: REFLECTIONS AND TRANSLATIONS

                Translations and reflections are geometric transformations that create images.  Foundations in Math  p. 315 – note well the information presented in the gray section.  Be sure to note the rules for reflections and translations.  Do # 1 to 3 at the bottom of p. 315, and # 4,5,6 at the top of p. 316.  Study #10 at the bottom of p. 316 very carefully. 

In Finish Line  book, note well information presented on p. 104.  Complete pp 105 to 111.  All of the information on the above pages should present you with the ability to complete the following question: (In your notebooks) Describe how to reflect a figure over each axis.  Use a triangle to illustrate your explanation. Also describe the effect of transposing the x and y coordinates of the vertices of a triangle.  Again, use an illustration to demonstrate your answer. 

VERIFYING PROPERTIES OF REFLECTIONS AND TRANSLATIONS:

                The essential question here is

“What are the important properties of reflections and translations?”

Progress in Math – After reading pp204-207, note well the questions from the guided practices pp.208 & 209. 

Upon completion of all the above work go to lesson 24 in Practice Coach p. 192 and complete all pages from 192 through 199.

 

ROTATIONS – Review and reinforce the information on rotations from the Khan Academy youtube.  Remember that in rotating a figure, we think of a rotation as clockwise or counterclockwise at 90 degrees , 180 degrees or 270 degrees.  Remember to carefully note the rules presented for both clockwise and counterclockwise and the application of these rules. (Teacher presentation)

Using various “coached examples” from the handout complete all questions dealing with rotations.

From Finish Line book review p. 112 and complete pp. 113 to 115.

VERIFYING PROPERTIES OF ROTATIONS:

Progress in Math – p.212 and 213

Foundations in Math – p.317 – note well rules presented in the gray section.  Do #1-6 on p.317 and

 # 7,8,9, 12,13 on p.318

 

DILATIONS Review and reinforce the information on dilations from the Khan Academy youtube.

Practice Coach Plus book – lesson 25 – Do pp 201 through 207

Finish Line Book – note well information on p.116 – Do pp. 117-118-119

REVIEW INFORMATION ON COORDINATE GEOMETRY

Common Core Coach Book – p.108, 109, 112, 113, 117, 118 (#1-6 on 118), 122 #1-6.

Progress Monitor – Benchmark 1 Book A.  Be sure to have the checked-off questions that deal with transformational geometry.  Remember that you will be given the answer to the multiple choice question and you are to prove how that answer is correct by doing the sequence of transformations.  

EXPLORING ANGLES OF TRIANGLES

INTRODUCTION TO CALCULATING THE MEASURE OF ANGLES ALGEBRAICALLY

  1. Using the “handout” be sure to note these terms and understand their meaning:

Similar triangles, corresponding angles, corresponding sides, angle, angle similarity theorem, exterior angle, remote interior angle, supplementary angle, complimentary angle.

  1. Note well the examples on p. 243(handout) – the relationship between remote interior angles and exterior angle.
  2. Do the Coached example on p. 244
  3. Lesson – 27   Coach Book – Explain 2 methods from p. 216
  4. Apply ( p.217) Show and explain your work. Complete p. 218, 219, 220, 221
  5. Complete p. 222,223 – for overall review of content