Unit 1, Lesson 15

Symmetry

Integrated Math 1

Practice

1. Problem 1

   For each figure, identify any lines of symmetry the figure has.

   

   

   

    

2. Problem 2

   In quadrilateral , and . The line is a line of symmetry for this quadrilateral.

   

   1. Based on the line of symmetry, explain why the diagonals and are perpendicular.
   2. Based on the line of symmetry, explain why angles and have the same measure.

3. Problem 3

   ForLesson 14: Defining Rotations

   Three line segments form the letter Z. Rotate the letter Z counterclockwise around the midpoint of segment by 180 degrees. Describe the result.

   

4. Problem 4

   ForLesson 14: Defining Rotations

   There is a square, , inscribed in a circle with center . What is the smallest angle we can rotate around so that the image of is ?

5. Problem 5

   ForLesson 9: Speedy Delivery

   Points , , , and are vertices of a square. Point  is inside the square. Explain how to tell whether point is closer to , , , or .

6. Problem 6

   ForLesson 11: Defining Reflections

   Lines and are perpendicular.

   Sometimes reflecting a point over has the same effect as rotating the point 180 degrees using center . Select all labeled points which have the same image for both transformations.

   

   Perpendicular lines l and m, intersecting at Point P. Line L goes through A, P and E. Line M goes through B and P. Points D and C are to the right of point M. Point D sits above L, Point C sits below L.

   1. A

   2. B

   3. C

   4. D

   5. E

7. Problem 7

   ForLesson 13: Incorporating Rotations

   Here is triangle . Match the description of the rotation with the image of under that rotation.

   

   1. Rotate 60 degrees clockwise around .

   2. Rotate 120 degrees clockwise around .

   3. Rotate 60 degrees counterclockwise around .

   4. Rotate 60 degrees clockwise around .

   1. 

      Triangle P prime O prime G prime on an isometric grid. Point O prime faces downwards and to the left, P prime faces upwards, G prime faces downwards and to the right.  

   2. 

      Triangle P prime O prime G prime on an isometric grid. Point O prime faces upwards and to the right, P prime faces downwards, G prime faces upwards and to the left.  

   3. 

   4.