CONGRUENCE AND TRANSFORMATIONS (GET GRAPH PAPER WHEN YOU ENTER CLASS) SECTION 4.4.

Slides:

Advertisements

Similar presentations

An isometry is a transformation that does not change the shape or size of a figure. Reflections, translations, and rotations are all isometries. Isometries.

Advertisements

Transformations Vocabulary.

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Transformations on the Coordinate Plane

A transformation is a change in the position, size, or

Rigid Motion in a Plane Reflection

Unit 7 Lesson 8.7: Dilations

Congruence and Transformations

Objectives Identify reflections, rotations, and translations.

Objectives Define and draw lines of symmetry Define and draw dilations.

9.1—Translations Course: Geometry pre-IB Quarter: 3rd

Term Transformation Describe The change in the position of a geometric figure, the pre-image, that produces a new figure called the image Representation.

An operation that moves or changes a geometric figure (a preimage) in some way to produce a new figure (an image). Congruence transformations – Changes.

Rigid Motion in a Plane Chapter 9 Section 1.

Congruence and Transformations

Objective Identify and draw dilations..

A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar. A A’

4-1 Congruence and transformations. SAT Problem of the day.

Holt Geometry 12-1 Reflections 12-1 Reflections Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Lesson 2.7 Objective: To complete dilations on a coordinate plane.

Dilations Advanced Geometry Similarity Lesson 1A.

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

1.4 Rigid Motion in a plane Warm Up

Chapter 6 Graphing & Describing “Dilations”. Section 1:Congruency transformations vs Similarity transformations. Section 2:Graphing a dilation. Section.

TRANSFORMATIONS. DEFINITION  A TRANSFORMATION is a change in a figure’s position or size.  An Image is the resulting figure of a translation, rotation,

Congruence and Transformations

 A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another.

Using Properties of Transformations to Show Congruence VOCABULARY.

UNIT 10 NOTES Dilations. Rigid Transformations ⇢ Congruence Reflections Rotations Translations Compositions Isometry!!!!!

Holt McDougal Geometry 9-1 Reflections 9-1 Reflections Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt.

Holt McDougal Geometry 4-1 Congruence and Transformations 4-1 Congruence and Transformations Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.

Sect. 7.1 Rigid Motion in a Plane

Objectives Draw, identify, and describe transformations in the coordinate plane. Use properties of rigid motions to determine whether figures are congruent.

12-7 Dilations.

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Warm up Identify the transformation ∆RST → ∆XYZ.

Congruence and Transformations on the coordinate plane

Constructions of Basic Transformations

Composition of Isometries & Dilations

Congruence and Transformations

Every segment is congruent to its image.

Every segment is congruent to its image.

Objectives Identify reflections, rotations, and translations.

Warm-up Test Review.

Congruence and Transformations

9-1 Translations.

Transformations Learning Target: I will be able to translate, reflect, rotate, and dilate figures.

Transformations Sections

Congruence and Transformations

Congruence and Transformations

Congruence and Transformations

If f(x) = 2x−5, then what is the value of f(2) + f(5) ?

Unit 1: Transformations Day 3: Rotations Standard

Transformation Notes 6.07.

4.1: Congruence and Transformation

9-6 Dilations 9-7 Similarity Transformations

9.1: Reflections.

TRANSFORMATIONS Translations Reflections Rotations

Students will be able to define and apply translations.

These are flips, slides, turns, and enlargements/reductions.

Unit 4 Transformations.

Congruence and Transformations

4.1: Dilations and Similar Triangles Tonight’s Homework: 4.1 Handout

Objectives Draw, identify, and describe transformations in the coordinate plane. Use properties of rigid motions to determine whether figures are congruent.

Warm-Up 2. What type of symmetry does the figure to the right have? How do you know?

Objective Identify and draw reflections..

7.1 Rigid Motion in a Plane.

Presentation transcript:

CONGRUENCE AND TRANSFORMATIONS (GET GRAPH PAPER WHEN YOU ENTER CLASS) SECTION 4.4

Plot the following points on the coordinate plane: Label each point. A (0,3) B(2,4) C(-2,0) D(-3,-5) E(4,-2)

A transformation is a change in the position or size of a figure. Some transformations are: Translations (slides) Reflections (flips) Rotations (turns) Dilations (changes size)

An Isometry or rigid transformation is a transformation that preserves length, angle measure and area. The image is congruent to the pre-image. Translations, reflections, and rotations are all rigid transformations. The image is CONGRUENT to the pre-image. A dilation changes the image with a scale factor so this is not a rigid transformation. The image is SIMILAR to the pre-image.

IF YOU ENLARGE THE IMAGE, THE SCALE FACTOR IS GREATER THAN ONE. IF YOU REDUCE THE IMAGE, THE SCALE FACTOR IS LESS THAN ONE. DILATION

Apply the transformation M to the polygon with the given vertices. Then identify and describe the transformation. 1. M: (x,y) (x+2, y – 5) P(1,2), Q(4,4), R(4,2) 2. M: (x,y) (-x,y) A(1,1), B(3,2), C(3,5)

3.M: (x,y) (-y,x) R(1,2), E(1,4), C(5,4), T(5,2) 4. M: (x,y) (2x,2y) K(-1,2), L(2,2), N(1,3)

Determine whether the figures are congruent. Then state the type of transformation and describe it. Give the rule. 1.A(1,1), B(4,1), C(4,3) vs. P(-4,2), Q(-1,2), R(-1,4) 2. A(2,2), B(-4,4), C(2,4) vs. P(3,3), Q(-6,6), R(3,6)

3. A(2,-1), B(3,0), C(2,3) vs. P(1,2), Q(0,3), R(-3,2) 4. A(-2,-2), B(-4,-1), C(-1,-1) vs. T(2,2), U(4,1), V(1,1) 5. A(-4,4), B(-4,6), C(2,6), D(2,4) vs. W(-2,2), x(-2,3), Y(1,3), Z(1,2)

SECTION QUIZ 1.Can a scale factor rule multiply x and y by different numbers? 2..