Unit 3 Resources & Lessons
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Daily Lesson Slides
Day 0: Introduction to Graphing
View/Print NotesDay 1: Lines & Point Symmetry
View/Print SlidesDay 2: Reflections & Rotations
View/Print SlidesDay 3: Translations & Dilations
View/Print SlidesDay 4: Sequences of Transformations
View/Print SlidesUnit 3: How to Guide
View/Print Guide
Day 1: Lines & Point Symmetry
Objective: To define and identify line symmetry and point symmetry in geometric figures.
Concept: Line Symmetry
A figure has line symmetry (or reflectional symmetry) if you can draw a line that divides the figure into two mirror images. This line is called the line of symmetry.
Concept: Point Symmetry
A figure has point symmetry if it looks the same after a 180° rotation around a central point. Every point on the figure has a corresponding point the same distance from the center, in the opposite direction.
I Do: Examples
- A square has 4 lines of symmetry and also has point symmetry.
- A rectangle (that is not a square) has 2 lines of symmetry and point symmetry.
- The letter H has two lines of symmetry and point symmetry.
- The letter A has one line of symmetry but no point symmetry.
Practice
How many lines of symmetry does a regular pentagon have?
Does the letter 'Z' have point symmetry? (Yes/No)
Day 2: Reflections & Rotations
Objective: To perform reflections and rotations on the coordinate plane.
Concept: Reflections (A Flip)
A reflection flips a figure across a line. Common reflection rules:
- Across the x-axis: \( (x, y) \rightarrow (x, -y) \)
- Across the y-axis: \( (x, y) \rightarrow (-x, y) \)
- Across the line y = x: \( (x, y) \rightarrow (y, x) \)
Concept: Rotations (A Turn)
A rotation turns a figure around a center point. Common counter-clockwise rotations about the origin (0,0):
- 90° rotation: \( (x, y) \rightarrow (-y, x) \)
- 180° rotation: \( (x, y) \rightarrow (-x, -y) \)
- 270° rotation: \( (x, y) \rightarrow (y, -x) \)
Practice
Reflect point A(3, -5) across the y-axis. A' = ()
Rotate point B(-2, 6) 180° about the origin. B' = ()
Day 3: Translations & Dilations
Objective: To perform translations and dilations on the coordinate plane.
Concept: Translations (A Slide)
A translation slides every point in a figure the same distance and direction. The rule is written as \( (x, y) \rightarrow (x+a, y+b) \), where 'a' is the horizontal shift and 'b' is the vertical shift.
Concept: Dilations (A Resize)
A dilation changes the size of a figure. The rule for a dilation centered at the origin is \( (x, y) \rightarrow (kx, ky) \), where 'k' is the scale factor.
- If \(|k| > 1\), it's an enlargement (gets bigger).
- If \(0 < |k| < 1\), it's a reduction (gets smaller).
Practice
Translate point C(8, 2) using the rule \( (x, y) \rightarrow (x-5, y+3) \). C' = ()
Dilate point D(4, -6) by a scale factor of 0.5. D' = ()
Day 4: Sequences of Transformations
Objective: To perform a sequence of multiple transformations and understand the difference between congruent and similar figures.
Concept: Composition of Transformations
This is when you apply more than one transformation to a figure. It's important to perform them in the order they are given, as the order can change the final result.
Concept: Congruence vs. Similarity
Two figures are...
- Congruent: If one can be mapped onto the other using only rigid motions (translations, reflections, rotations). They are the same shape and same size.
- Similar: If one can be mapped onto the other using rigid motions AND dilations. They are the same shape, but different sizes.
Practice
Point E is (2, 3). Reflect it over the x-axis, then translate it by \( (x,y) \rightarrow (x+1, y-4) \). What is the final coordinate E''? ()
If a figure is rotated and then dilated, is the new figure congruent or similar to the original?
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