1. Topic 1: Transformations and Congruence & Geometry Notation
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Topic 1: Transformations and Congruence & Geometry Notation
Unit 1 – Transformations and Congruence
Module 1: Tools of Geometry
1.1 Segments, Lengths, and Midpoints
1.2 Angle Measures and Angle Bisectors
1.3 Representing and Describing Transformations
1.4 Reasoning and Proof
Module 2: Transformations and Symmetry
2.1 Translations
2.3 Rotations
2.2 Reflections
2.4 Investigating Symmetry
Module 3: Congruent Figures
3.1 Sequence of Transformations
3.2 Proving Figures are Congruent Using Rigid Motions
3.3 Corresponding Parts of Congruent Figures are Congruent

2. Day 2

3. Explain 1: Postulates
A postulate is a statement that is accepted as true without proof

7. Explain 2: Distance Between Points
Always Sketch

10. Explain 3: Finding Midpoint

11. Explain 4: Midpoint Formula

14. 1.1 Classwork
Honors: 5, 9, 12, 13, 15-20, 22,24, 28, 29
Regular: 5, 9, 13, 17-20, 22, 23,
Both: Send a picture to Dropbox of a point, a line, a line segment, and a plane in your home or your community.
Both: Copy Do Now #2 Notes from website in composition notebook
Reminders:
Summer Assignment Due Friday
Electronic Class Contract due Aug 29th
Index Card Due Monday
Bring Tablets on Friday last day of week
Once a week: MANDATORY online homework

15. Day 3/4

16. Explain 1: Naming Angles

17. Construction? Watch video on teacher website.

18. Explain 2: Measuring Angles
Distance around a circular arc is undefined until a measurement unit is used
Degrees (°) is a common measurement for arcs.
There are 360° around a circle
1° is 1/360 of a circle
The measurement of an angle is written as m∠𝐴 𝑜𝑟 °m∠𝑃𝑄𝑅

22. Explain 3: Angle Bisectors

23. Construction? Watch video on teacher website.

26. Day 3/4

27. Explain 1: Introducing Proofs
A Conditional statement is a statement that can be written in the form “if p, then q” where p is the hypothesis, and the q is the conclusion
“If 3𝑥=5=13, then 𝑥=6”
Most Properties of Quality can be written as a conditional statements.

28. This Photo by Unknown Author is licensed under CC BY

31. Explain 2: Using Postulates about Segments and Angles
Recall supplementary angles add up to 180°.
A type is called a linear pair
A linear pair is a pair of adjacent angles whose non common sides are opposite pairs.

35. Explain 3: Using Postulates about Lines and Planes (Part 1)

36. Explain 3: Using Postulates about Lines and Planes (Part 2)

39. 1.2/1.4 Classwork
Honors: Evaluate 1.2: 5,6,7,9, 12, 15, 16, 20, 21, Evaluate 1.4: 5,6,8, 11, 17, 19, 23, 24, 26, 28
Regular: Evaluate 1.2 4,5,6,7,8,12, 15, Evaluate 1.4: 5, 6, 11, 17, 19, 23, 26
Both: Copy Do Now #3 Notes from website in composition notebook
Reminders:
Summer Assignment Due Friday
Electronic Class Contract due Aug 29th
Index Card Due Monday

40. The input of a transformation od the preimage, like A
Day 5
Vocabulary:
A transformation is a function that changes the position, shape, and/or size od a figure
The input of a transformation od the preimage, like A
The output is the image, like A’ (A prime)
Translation, reflections and rotations are three types of transformation.

41. Transformation Example

42. Explain 1: Rigid vs Nonrigid
Some transformations preserve length and angle measure, others do not
A rigid motion changed position without affecting size or shape of the figure.
Examples: translation, reflections, and rotations
Steps:
Look for patters in the coordinates
Compare lengths of the preimage and image of corresponding segments
Compare angles of corresponding angles

43. Recall Finding Distance

44. Recall Finding Distance

46. Explain 2: Non Rigid Motions
A nonrigid motion do not preserve distance between points.
Examples: stretch, compression (dilations)
Steps:
Look for patterns in the coordinates (usually multiplication)
Compare lengths of the preimage and image of corresponding segments

50. 1.3 Classwork
Honors: 1, 3, 5, 10, 15, 16, 17
Regular: 2, 4, 5, 10, 15,
Both: Copy Do Now #4 Activity Questions (BUT DO NOT SOLVE THEM) from website in composition notebook
Reminders:
Summer Assignment Due Friday
Electronic Class Contract due Aug 29th
Index Card Due Monday

51. Translations, Rotations, Reflections: The Basics
Day 6/7
Translations, Rotations, Reflections: The Basics
Lecture: Just watch. Pencils Down. Short Notes 4 Your Turns KAHoOOOooT!!

52. In geometry, a transformation is a way to change the position of a figure.

53. In some transformations, the figure retains its size and only its position is changed.
Examples of this type of transformation are:
translations, rotations, and reflections
In other transformations, such as dilations, the size of the figure will change.(this will be discussed later)

54. A TRANSLATION IS A SLIDE
Basically, translation means that a figure has moved.
An easy way to remember what translation means is to remember…
A TRANSLATION IS A SLIDE
A translation is usually specified by a direction and a distance, AKA a vector.

55. A REFLECTION IS FLIPPED OVER A LINE.
A reflection is a transformation that flips a figure across a line.
A REFLECTION IS FLIPPED OVER A LINE.

56. reflectional symmetry.
Sometimes, a figure has
reflectional symmetry.
This means that it can be folded along a line of reflection within itself so that the two halves of the figure match exactly, point by point.
Basically, if you can fold a shape in half and it matches up exactly, it has reflectional symmetry.

57. REFLECTIONAL (LINE) SYMMETRY
Line of Symmetry
The line of reflection in a figure with reflectional symmetry is called a line of symmetry.

58. How many lines of symmetry does each shape have?
Your Turn
How many lines of symmetry does each shape have?
Do you see a pattern?

59. ROTATION
A rotation is a transformation that turns a figure about (around) a point or a line.
Basically, rotation means to spin a shape.
The point a figure turns around is called the center of rotation.
The center of rotation can be on or outside the shape.

60. What does a rotation look like?
center of rotation
A ROTATION MEANS TO TURN A FIGURE

61. ROTATIONAL SYMMETRY
A shape has rotational symmetry if, after you rotate less than one full turn, it is the same as the original shape.
As this shape is rotated 360, is it ever the same before the shape returns to its original direction?
Yes, when it is rotated 90 it is the same as it was in the beginning.
So this shape is said to have rotational symmetry.
90
The angles of rotation are:
360° 4 =90°, 180°, 270°
Divide by how many times the shape is the same after a full rotation then add that until you reach 360.

62. CONCLUSION FLIP REFLECTION SLIDE TRANSLATION TURN ROTATION
We just discussed three types of transformations.
See if you can match the action with the appropriate transformation.
FLIP
REFLECTION
SLIDE
TRANSLATION
TURN
ROTATION

63. Putting Lines of Symmetry and Rotational Symmetries Together.
ONE EXAMPLE 4 Your Turns KAHoOOOooT!!

68. Transformations Part 1 Classwork
Honors: (Evaluate 2.4) 2,3,4,6,7,8,10,10,13,16
Regular: (Evaluate 2.4) 2,4,7,8,14, 16
Both: Copy Do Now #5 Notes from website in composition notebook
Reminders:

69. Transformations on Coordinate Plane
Day 8/9
Lets talk Math
Transformations on Coordinate Plane

70. Translations as Vectors
A vector is a ray that has direction and length
Tell you how far to go and where (up/down then left/right)
Vectors have a starting point, called initial point, and an ending point, called terminal point.
Vector symbols have a half arrow above then, 𝑣 , this is called vector v. OR they can be written like <4,2>
How could vectors be connected to translations?

71. Explain 1: Translations

72. Explain 2: Translation in Coordinate Plane
Vector <5,3>
This is
“a”
Left/right
This is
“b”
Up/down
Getting NEW Point from OLD point:

73. Verbal Description:
Function Description:
Step 1: Copy Vector on every vertex
Step 2: Draw Segments
Δ 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝑖𝑠
𝑡ℎ𝑒
𝑖𝑚𝑎𝑔𝑒 𝑜𝑓 Δ𝐴𝐵𝐶

74. Verbal Description:
Function Description:

75. Verbal Description:
Function Description:

78. Honors: Both Regular: #5

79. Explain 3: Identifying the Vector

80. When will your Reflection show who you are?

81. Explain 1: Reflect using Perpendicular Bisectors
Points of Preimage and reflected image must me equidistant from the line of reflection.
This distance bisects the line of reflection

85. Explain 2: Reflections as Coordinate Points

89. Explain 3: Find the Line of Reflection
To find the line of reflection, look for the midpoint between corresponding points.
Why does this work?

91. Rotations

92. Explain 2: Rotations as Coordinate Points
When not specified, assume Counterclockwise

93. (About the Origin)

96. Rotations NOT about the Origin

97. Video

98. Your Turn
Rotate Triangle about the point (1,−1)

99. Transformations Part 2 Classwork
Honors: Evaluate 2.1: Evaluate 2.2: Evaluate 2.3:
Regular:
Both: Copy Do Now #6 Activity ( BUT DO NOT SOLVE) from website in composition notebook
Reminders:

100. Day 10

101. Explain 1: Combining Rigid Transformations
(𝑥+4,𝑦+1)

102. (𝑥+5,𝑦+1)

104. Explain 2: Combining Non-rigid

106. Explain 3: Predict the effect of the Transformations
-Say what happens to the shape and the (possibly) new location of the shape

107. (as a class discussion)

108. 3.1 Classwork --> Homework
Honors: 2-5, 8,13-19,23, when there are vector, write out both verbal and coordinate point meaning. Regular: 2,4, 5, 13-19
 when there are vector, write out both verbal and coordinate point meaning.
Copy Do Now Notes #7
Reminders: ….

109. Day 11/12

110. Explain 1: Determining Congruence

112. Explain 2: Find Sequence of Rigid Motions

114. Explain 3: Investigating Congruent Segment and Angles

116. Day 11/12

117. Explain 1: Corresponding Parts of Congruent Figures are Congruent

119. Explain 2: Applying the Properties of Congruence
Rigid Motions Preserve length and measure
Congruent Figures
Same Math Value in length or degree
𝐴𝐵 ≅ 𝑋𝑌
𝐴𝐵=𝑋𝑌
⦟𝐽≅⦟𝐾
𝑚⦟𝐽=𝑚⦟𝐾
Remember “=“ and “𝑚⦟” are only used when numbers are involved

123. Explain 3: Using Congruent Corresponding Parts in a Proof
This is called a table proof.

127. 3.3 Classwork --> Homework
Honors: 3.2: 2,5, 8,13,15,19, : 2, 3, 7, 10, 15, 20, 21, Discovering Geometry Page 252-3: ,11,25,26,29,30 Regular: 3.2: 2,8,13, : 2, 3, 6,7,10, Discovering Geometry Page 252-3: 7,25,29 (tip given on 29)
Copy Do Now Notes #7
Reminders: ….