1. Congruence and Similarity
Congruent means same shape and same size.
Angles, segments and shapes can be congruent.
Similar means same shape.

2. What is graphic design
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3. Movement on the coordinate plane
Preimage is the original image. Points on the Pre-image are indicated by capital letters. A,B,C
Image is the image that came from the pre-image. Points on the image are indicated by primes. A’ B’ C’

4. Ways to transform a shape on a coordinate plane.
Translation (Slide all points of a shape same distance and direction.)
Reflection (flip all points on a shape over a line)
Rotation (turn all points on a shape about a point)

5. Describing a Translation
Description in words
The preimage was translated 6 units to the left.
Description using coordinate notation.
(x,y)→(x-6,y)

6. Describing a Translation
Description in words.
Coordinate notation

7. Describing a Translation
Description in words.
Coordinate notation

8. Describing a Translation
Description in words.
Coordinate notation

9. Important concepts about a translation
Translation is a movement of all points of a shape in the same ________and the same _______
A translated shape maintains its shape and size. In other words the image and the pre-image are ___________.
All segments drawn from corresponding points on the image and pre-image are ______
All corresponding line segments are ____________

10. Translating a linear function
Sue makes 5 dollars an hour. Sue makes 5 dollars an hour with a one time bonus of 10 dollars.

11. Write a new equation based on the translation.
Translate 3 units down Y=2x
Translate 4 units up y = -x
Translate 2 units up y = 2x+1
Translate 5 units down y= 3x+2

12. Reflection.

13. Describing a reflection.
Description in words
Description as coordinate notation.

14. Describing a reflection
Description in words
Description as coordinate notation.

15. Describing a reflection
Description in word
Coordinate notation

16. Describing a reflection
Description in words
Coordinate notation

17. Describing a reflection
Description in words

18. Describing a reflection
Description in words

19. Important concepts about reflection
A point on the pre-image is the same distance to the line of reflection as a point on the image.
Line segments connecting corresponding points are bisected at the line of reflection.

20. Rotation 7.3
Rotation in real life Car parts/ Mechanics Clock Body motion Astronomy Weapons Fans Amusement park rides
Rotation vocabulary
Point of rotation
Angle of rotation

21. Rotation Describing a rotation in words
I am rotating about the origin. 90 degrees counter clockwise.
Describing a rotation with coordinate notation.
Preimage
Image A
(2,3)
(-3,2) B
(4,3)
(-3,4) C
(4,0)
(0,-4)
Rule
(x,y)
( , )

22. Rotation and circles
What do you notice about rotation when circles are drawn about the point of rotation.
How do you know this is a 90 degrees rotation counterclockwise?
Does a rotation change the shape or size of the triangle?

23. 90 degree rotation and the hook
The hook method.
Vertical lines become horizontal lines.
Horizontal lines become vertical lines.

24. Rotate 90 degrees counterclockwise about the origin using the hook method.
Give the new coordinates for A’,B’ and C’ to your neighbor.

25. Rotate 90 degrees counterclockwise about the origin using the hook method.
Give the new coordinates for A’,B’ and C’ to your neighbor.

26. Rotating objects a different number of degrees.
I can rotate this object 120 degrees about the origin using technology.

27. Rotating objects in intervals of 90 degrees around points other than the origin.

28. Rotating objects in intervals of 90 degrees around points other than the origin.
Rotate 90 degrees cc about the point C.
of changing your vertical lines to horizontal lines and your horizontal lines to vertical lines.

29. Activity Draw a pre-image on a coordinate plane. Label the vertices.
Then take the image through a translation, a reflection and a rotation in any order.
Write rules for each transformation. Write coordinates for each transformation.

30. Activity with Paddy Paper
Draw a shape on the coordinate plane.
Trace the shape on paddy paper.

31. I can map one object onto another through multiple transformations.

32. Describe the transformations that would map one triangle onto another
Compare the coordinates

33. Describe the transformations that would map one triangle onto another

34. Describe the transformations that would map one triangle onto another

35. Activity with geogebra
See if you can use geogebra to replicate the transformations that took place from the pre-image to the image. Then

37. Triangle congruence Shortcuts

38. All I need are three pairs of congruent side lengths and a compass to prove sss congruency.

39. If SSS works for triangle congruency does AAA work
If SSS works for triangle congruency does AAA work for triangle congruency
If SSS works for triangle congruency does SSA work?

40. Two triangles are congruent if all corresponding sides are the same length SSS
How can I tell if the corresponding sides are the same length?

41. http://nlvm. usu. edu/en/nav/fra mes_asid_165_g_1_t_3. html
mes_asid_165_g_1_t_3.html?op en=instructions&from=topic_t_3 .html

42. Two triangles are congruent if all corresponding sides are the same length SSS
What tool am I using here to show that all the corresponding side lengths are congruent?
Explain to your friend how to use this tool to determine congruent side lengths.

43. Two triangles are congruent if all corresponding sides are the same length SSS
What kind of transformations took place from the preimage ABC to the image EDF?
Did the side lengths change through transformations?

44. Two triangles are congruent if all corresponding sides are the same length SSS
Write a congruency statement for the two triangles in the graph at the right?
How do you know the two triangles are congruent?
Can you come up with a second way to determine triangle congruence?

45. Two triangles are congruent if all corresponding sides are the same length SSS
Given
AB and DE are congruent
BC and EF are congruent
D is the midpoint of AC
C is the midpoint of DF
Are the two triangles congruent? Explain your reasoning.

46. Two triangles are congruent if all corresponding sides are the same length SSS
BD is a perpendicular bisector?
Are the triangles congruent?
Explain your reasoning.

47. Two triangles are congruent if two pairs of corresponding sides and the included angle are congruent. SAS
You may remember the triangle inequality theorem which states that the largest side of a triangle is opposite the largest angle.
If you completed both triangles to the right AC would be the same length as DF. Likewise < B would be congruent to <E

48. Two triangles are congruent if two pairs of corresponding sides and the included angle are congruent. SAS
If BE is Congruent to CE and AD is Congruent to DE determine if the two triangles are congruent.
List the ways that you could determine congruence. 1. 2. 3. 4.

49. Two triangles are congruent if two pairs of corresponding sides and the included angle are congruent. SAS
If BD and AC are perpendicular and E is the midpoint of BD prove that BC is Congruent to CD.

50. Two triangles are congruent if two pairs of corresponding sides and the included angle are congruent. SAS
Can you solve for missing sides and angles of the two triangles?

51. How could you show that all the triangles in the regular hexagon are congruent?

52. 13.5 angle side angle (ASA)
IF two triangles have 2 pairs of congruent angles and an included side then they are congruent.
Using the diagram, can you explain why only one unique triangle can be created with 2 angles and an included side?

53. 13.6 Angle Angle Side (AAS)
Two triangles are shown to be congruent using the ASA postulate. How can we conclude that the AAS postulate would also work based on the ASA postulate?

54. Postulate SU + UT = ST Postulate is a common sense idea Examples
A linear pair contains 180 degrees
2 line segments can be added together to get one large segment
SU + UT = ST

55. Theorem
A theorem is a rule in math that has been proven by using postulates, definitions, and other theorems.
Prove the vertical angles theorem. In other words show that x and z are congruent
Statement Reason
<X+<Y = 180 Linear pairs are supplements
<Z + <Y = 180 Linear pairs are supplements
<Z+<Y= <X+<Y Substitution
<Z = < X Subtraction property of equality

56. Practice with triangle congruency proofs
Statement
Reason
AD is parallel to BC
given
AD = CB
<DAC = <BCA
Alternate interior angles
<BEC = <AEC
Vertical angles
∆𝐴𝐸𝐷=∆𝐶𝐸𝐵
AAS

57. Practice with triangle congruency proofs
Statement
Reason
Given
<JKM =90 and <LKM=90
<JKM and <LKM are congruent
∆𝐽𝐾𝑀≅∆𝐿𝐾𝑀

58. Practice with triangle congruency proofs
Statement
Reason
given
Reflexive property
SAS

59. Practice with triangle congruency proofs
Statement
Reason
B is midpoint of DC
AB is perpendicular to DC
DB = BC
AB=AB
<ABC and <ABD = 90
<ABC is congruent to <ABD
∆𝐴𝐵𝐷≅∆𝐴𝐵𝐶

60. Practice with triangle congruency proofs
Statement
Reason
Given
FG= GH
EG=EG
SSS
<1 = <2
CPCTC

61. Practice with triangle congruency proofs
Statement
Reason