1. Transformations Similarity and Congruence
UMI: July 19, 2016

2. Transformation
A transformation is a process which changes the position (and possibly the size and orientation) of a shape. There are four types of transformations:
Rotation (Turn)
Reflection (Flip)
Translation (Slide)
Enlargement (Resize)

3. Rotation (Turn)
Rotation (also known as Turn) The distance from the center to any point on the shape stays the same.
Every point makes a circle around the center.
Changes the orientation of the shape
Changes the position of the shape
Everything else stays the same.

4. Four Quadrants
The x and y axes divide the space up into 4 pieces: Quadrants I, II, III and IV(They are numbered in a counterclockwise direction)

5. Example:
Rectangle A′B′C′D′ is the image of rectangle ABCD after which of the following rotations? Find the new coordinate of the A′B′C′D′
A 90° clockwise rotation about the origin
A 180° rotation about the origin
A 90° counterclockwise rotation about the origin

6. Solution: Solution: C is correct.
By joining A and A′ to the origin O, it is clear that this is a 90° counterclockwise rotation about the origin. The same distance from the origin.(Do the same for the other points and their images to see for yourself).
The new coordinate is −1,2 , −3,2 , −3,5 , −1,5

7. Practice 1:
The square is rotated one complete turn about the point O. Which of the following shows the new position of the square?

8. Practice 2:
The square is rotated about the point O. Which of the following shows the new position of the square? Find the new coordinate of the square.

9. Practice 3:
When this 'L'-shape is rotated about the origin (0,0) by 90°counterclockwise, which one of these would it look like?

10. Reflection(Flip)
Reflection (also known as Flip) in a line produces a mirror image in which corresponding points on the original shape and the mirror image are always the same distance from the mirror line.
Every point is the same distance from the central line !
The reflection has the same size as the original image
The central line is called the Mirror Line 

11. How Do I Do It Myself?
Measure from the point to the mirror line (must hit the mirror line at a right angle)
Measure the same distance again on the other side and place a dot.
Then connect the new dots up!

12. Practice 1:
The square is flipped across the line L. Which of the following shows the new position of the square?

13. Practice 2:
The square is flipped across the line L. Which of the following shows the new position of the square?

14. Similar
Two shapes are Similar when the only difference is size (and possibly the need to move, turn or flip one around).
Similar figures 
have equal corresponding angles
the length of their corresponding sides have equal ratios

15. Determine whether the polygons are similar. Justify your answer
Example:
Determine whether the polygons are similar. Justify your answer
Solution :
4 3 = 8 6 = 4 3 = 8 6 , the measures of the sides of the polygons are proportional.
The corresponding angles are not equal.
Therefore, the polygons are not similar.

16. Determine whether the polygons are similar. Justify your answer
Example:
Determine whether the polygons are similar. Justify your answer
Solution :
The corresponding angles are equal.
= = = , the measures of the sides of the polygons are proportional.
Therefore, the polygons are similar.

17. Example: Solution : The triangles are similar. Find the value of x
Write proportions using corresponding parts. Then solve to find the missing measure
𝑥 4 = 4 8
Solve 𝑥=2

18. Congruent
If one shape can become another using Turns, Flips and/or Slides, then the shapes are Congruent. 
Congruent figures 
The same size
The same shape.
They are similar figures that are equal in size

19. Example:
These figures are congruent. Find the measure of angle I.
Solution :
Since the figures are congruent, all angles have the same measure.
According to the figures; m∠𝑄= 42 𝑜 ,𝑠𝑜 𝑚∠𝐼= 42 𝑜

20. Example:
The two quadrilaterals are congruent. Which side in quadrilateral ABCD corresponds to WZ in quadrilateral WXYZ?
Solution :
WZ faces the angles marked with two arcs and four arcs.
DA also faces the angles marked with two arcs and four arcs.
So DA corresponds to WZ.

21. Thank You References: A problem solving approach to mathematics
for elementary school teachers by Billstein,
Libeskind, Lott
Math is Fun :
Emathematics: